Systems and methods for time delay estimation
Embodiments described herein provide a method for time delay estimation in a wireless communication system. A signal received, from a transmitter, is delayed due to hardware components in the receiver. A time domain representation of a computed complex channel impulse response (CIR) is generated. A first set of peaks of a time domain representation of the complex CIR is determined and a first peak, having a lowest time delay of the first set of peaks relative to the arrival time of the signal at the receiver, is identified. Following the interpolation of a region corresponding to the first peak, a second set of peaks is determined, and a more accurate estimation of the delay experienced by the signal through the receiver is determined.
1. A method for time delay estimation in a wireless communications system, the method comprising:
receiving, from a transmitter, a signal, wherein the signal is delayed due to hardware components in a receiver;
computing, at the receiver, a complex channel impulse response (CIR) of the signal, wherein the complex CIR comprises an in-phase component and a quadrature component;
generating a time domain representation of the complex CIR;
determining a first plurality of peaks of the time domain representation of the complex channel impulse response (CIR);
identifying, from the first plurality of peaks, a first peak having a lowest time delay of the first plurality of peaks relative to an arrival time of the signal at the receiver;
interpolating, from the time domain representation of the complex CIR, a selection of data points adjacent to the first peak;
determining, from the interpolated selection of data points adjacent to the first peak, a second plurality of peaks; and
identifying, from the second plurality of peaks, a second peak indicative of a time delay estimate of delay caused by the hardware components in the receiver and having a lowest time delay of the second plurality of peaks relative to the arrival time of the signal at the receiver.
2. The method for time delay estimation of claim 1 , wherein determining the first plurality of peaks of the time domain representation of the complex CIR comprises:
determining, from the time domain representation of the complex CIR, the magnitudes of data points of the complex CIR indicative of a power of the complex CIR;
comparing the magnitudes of the data points of the complex CIR to a noise threshold; and
selecting the first plurality of peaks having magnitudes surpassing the noise threshold.
3. The method for time delay estimation of claim 1 , further comprising:
determining a data point of the complex CIR having the largest magnitude of data points of the complex CIR; and
determining, based on magnitudes of the data points of the complex CIR, that the data point of the complex CIR is a peak of the first plurality of peaks.
4. The method for time delay estimation of claim 1 , wherein interpolating, from the time domain representation of the complex CIR, the selection of data points adjacent to the first peak comprises:
interpolating a selection of data points of the in-phase component of the time domain representation of the complex CIR adjacent to the first peak; and
interpolating a selection of data points of the quadrature component of the time domain representation of the complex CIR adjacent to the first peak.
5. The method for time delay estimation of claim 4 , further comprising:
computing, based on the interpolated selection of data points of the in-phase component, the interpolated selection of data points of the quadrature component, a reconstructed time domain representation of the complex CIR; and
wherein determining, from the interpolated selection of data points adjacent to the first peak, the second plurality of peaks comprises:
determining a data point of the reconstructed time domain representation of the complex CIR having the largest magnitude of data points of the reconstructed time domain representation of the complex CIR; and
determining, based on decreasing magnitudes of data points adjacent to the data point, that the data point is a peak of the second plurality of peaks.
6. The method for time delay estimation of claim 4 , wherein determining the second plurality of peaks comprises:
determining a data point of the in-phase component adjacent to the first peak having the largest magnitude of data points of the in-phase component adjacent to the first peak;
determining, based on magnitudes of data points of the in-phase component adjacent to the first peak, that the data point of the in-phase component adjacent to the first peak is a peak of a third plurality of peaks of the in-phase component adjacent to the first peak;
determining a data point of the quadrature component adjacent to the first peak having the largest magnitude of data points of the quadrature component adjacent to the first peak; and
determining, based on magnitudes of data points of the quadrature component adjacent to the first peak, that the data point of the quadrature component is a peak of a fourth plurality of peaks of the quadrature component adjacent to the first peak.
7. The method for time delay estimation of claim 6 , wherein identifying the second peak indicative of the time delay estimate of the delay caused by the hardware components in the receiver and having the lowest time delay of the second plurality of peaks relative to the arrival time of the signal at the receiver comprises:
identifying a third peak of the third plurality of peaks having a lowest time delay of the third plurality of peaks relative to the arrival time of the signal at the receiver;
identifying a fourth peak of the fourth plurality of peaks having a lowest time delay of the fourth plurality of peaks relative to the arrival time of the signal at the receiver; and
determining the second peak using a weighted mean of respective time delays of the third peak and the fourth peak relative to the arrival time of the signal at the receiver.
8. The method for time delay estimation of claim 1 , wherein the first plurality of peaks amounts to a predetermined number of determined peaks.
9. The method for time delay estimation of claim 4 , wherein the first plurality of peaks comprises a plurality of peaks of the in-phase component and a plurality of peaks of the quadrature component and wherein determining the first plurality of peaks of the time domain representation of the complex CIR comprises:
separating the complex CIR into the in-phase component and the quadrature component;
determining a data point of the in-phase component having the largest magnitude of data points of the in-phase component;
determining, based on magnitudes of data points of the in-phase component, that the data point of the in-phase component is a peak of the plurality of peaks of the in-phase component;
determining a data point of the quadrature component having the largest magnitude of data points of the quadrature component; and
determining, based on magnitudes of data points of the quadrature component, that the data point of the quadrature component is a peak of the plurality of peaks of the quadrature component.
10. The method for time delay estimation of claim 9 , wherein identifying, from the first plurality of peaks, the first peak having the lowest time delay of the first plurality of peaks relative to the arrival time of the signal at the receiver comprises:
identifying a peak of the plurality of peaks of the in- phase component having a lowest time delay of the plurality of peaks of the in-phase component; and
identifying a peak of the plurality of peaks of the quadrature component having a lowest time delay of the plurality of peaks of the quadrature component.
11. A system for time delay estimation in a wireless communications system, the system comprising:
a receiver configured to:
receive, from a transmitter, a signal, wherein the signal is delayed due to hardware components in a receiver; and
control circuitry coupled to the receiver, the control circuitry configured to:
compute, at the receiver, a complex channel impulse response (CIR) of the signal, wherein the complex CIR comprises an in-phase component and a quadrature component;
generate a time domain representation of the complex CIR;
determine a first plurality of peaks of the time domain representation of the complex channel impulse response (CIR);
identify, from the first plurality of peaks, a first peak having a lowest time delay of the first plurality of peaks relative to an arrival time of the signal at the receiver;
interpolate, from the time domain representation of the complex CIR, a selection of data points adjacent to the first peak;
determine, from the interpolated selection of data points adjacent to the first peak, a second plurality of peaks; and
identify, from the second plurality of peaks, a second peak indicative of a time delay estimate of the delay caused by the hardware components in the receiver and having a lowest time delay of the second plurality of peaks relative to the arrival time of the signal at the receiver.
12. The system for time delay estimation of claim 11 , wherein the control circuitry is configured to determine the first plurality of peaks of the time domain representation of the complex CIR by:
determining, from the time domain representation of the complex CIR, the magnitudes of data points of the complex CIR indicative of a power of the complex CIR;
comparing the magnitudes of the data points of the complex CIR to a noise threshold; and
selecting the first plurality of peaks having magnitudes surpassing the noise threshold.
13. The system for time delay estimation of claim 11 , the control circuitry further configured to:
determine a data point of the complex CIR having the largest magnitude of data points of the complex CIR; and
determine, based on magnitudes of the data points of the complex CIR, that the data point of the complex CIR is a peak of the first plurality of peaks.
14. The system for time delay estimation of claim 11 , wherein the control circuitry is further configured to interpolate, from the time domain representation of the complex CIR, the selection of data points adjacent to the first peak by:
interpolating a selection of data points of the in-phase component of the time domain representation of the complex CIR adjacent to the first peak; and
interpolating a selection of data points of the quadrature component of the time domain representation of the complex CIR adjacent to the first peak.
15. The system for time delay estimation of claim 14 , the control circuitry further configured to:
compute, based on the interpolated selection of data points of the in-phase component, the interpolated selection of data points of the quadrature component, a reconstructed time domain representation of the complex CIR; and
wherein the control circuitry is configured to determine, from the interpolated selection of data points adjacent to the first peak, the second plurality of peaks by:
determining a data point of the reconstructed time domain representation of the complex CIR having the largest magnitude of data points of the reconstructed time domain representation of the complex CIR; and
determining, based on decreasing magnitudes of data points adjacent to the data point, that the data point is a peak of the second plurality of peaks.
16. The system for time delay estimation of claim 14 , wherein the control circuitry is configured to determine the second plurality of peaks by:
determining a data point of the in-phase component adjacent to the first peak having the largest magnitude of data points of the in-phase component adjacent to the first peak;
determining, based on magnitudes of data points of the in-phase component adjacent to the first peak, that the data point of the in-phase component adjacent to the first peak is a peak of a third plurality of peaks of the in-phase component adjacent to the first peak;
determining a data point of the quadrature component adjacent to the first peak having the largest magnitude of data points of the quadrature component adjacent to the first peak; and
determining, based on magnitudes of data points of the quadrature component adjacent to the first peak, that the data point of the quadrature component is a peak of a fourth plurality of peaks of the quadrature component adjacent to the first peak.
17. The system for time delay estimation of claim 16 , wherein the control circuitry is configured to identify the second peak indicative of the time delay estimate of the delay caused by the hardware components in the receiver and having the lowest time delay of the second plurality of peaks relative to the arrival time of the signal at the receiver by:
identifying a third peak of the third plurality of peaks having a lowest time delay of the third plurality of peaks relative to the arrival time of the signal at the receiver;
identifying a fourth peak of the fourth plurality of peaks having a lowest time delay of the fourth plurality of peaks relative to the arrival time of the signal at the receiver; and
determining the second peak using a weighted mean of respective time delays of the third peak and the fourth peak relative to the arrival time of the signal at the receiver.
18. The system for time delay estimation of claim 11 , wherein the first plurality of peaks amounts to a predetermined number of determined peaks.
19. The system for time delay estimation of claim 14 , wherein the first plurality of peaks comprises a plurality of peaks of the in-phase component and a plurality of peaks of the quadrature component and wherein the control circuitry is configured to determine the first plurality of peaks of the time domain representation of the complex CIR by:
separating the complex CIR into the in-phase component and the quadrature component;
determining a data point of the in-phase component having the largest magnitude of data points of the in-phase component;
determining, based on magnitudes of data points of the in-phase component, that the data point of the in-phase component is a peak of the plurality of peaks of the in-phase component;
determining a data point of the quadrature component having the largest magnitude of data points of the quadrature component; and
determining, based on magnitudes of data points of the quadrature component, that the data point of the quadrature component is a peak of the plurality of peaks of the quadrature component.
20. The system for time delay estimation of claim 19 , wherein the control circuitry is configured to identify, from the first plurality of peaks, the first peak having the lowest time delay of the first plurality of peaks relative to the arrival time of the signal at the receiver by:
identifying a peak of the plurality of peaks of the in- phase component having a lowest time delay of the plurality of peaks of the in-phase component; and
identifying a peak of the plurality of peaks of the quadrature component having a lowest time delay of the plurality of peaks of the quadrature component.