Apparatus and method for channel estimation using compressive sensing based on Taylor series expansion

• US 8,582,674 B2
• Filed: 11/19/2010
• Issued: 11/12/2013
• Est. Priority Date: 11/24/2009
• Status: Expired due to Fees

• Current Assignee: Qualcomm, Inc.
• Original Assignee: Qualcomm, Inc.
• Inventors: Yu, Yingqun, Abrishamkar, Farrokh, Wang, Ni-Chun, Shental, Ori
• Primary Examiner(s): Kim, Kevin
• Application Number:
  US12/950,435
• Publication Number:
  US 20110286507A1
• Time in Patent Office: 1,089 Days
• Field of Search: 375/260
• US Class Current: 375/260
• CPC Class Codes: H04L 25/0234 by non-linear interpolation
• CPC Class Codes: H04L 25/0242 using matrix methods
• CPC Class Codes: H04L 27/2607 Cyclic extensions
• CPC Class Codes: H04L 5/0048 Allocation of pilot signals, i.e. of signals known to the receiver

Abstract

An apparatus and method for channel estimation comprising determining a channel impulse response using a Taylor series expansion with a plurality of Taylor series coefficients; determining a channel frequency response based on the channel impulse response; collecting the channel frequency response over a plurality of symbols to obtain a composite channel frequency response; generating a sensing matrix based on the Taylor series expansion; and determining the plurality of Taylor series coefficients based on the composite channel frequency response and the sensing matrix using compressive sensing channel estimation.

Claims

1. A method for channel estimation comprising:

determining a channel impulse response using a Taylor series expansion with a plurality of Taylor series coefficients;

determining a channel frequency response based on the channel impulse response;

collecting the channel frequency response over a plurality of symbols to obtain a composite channel frequency response;

generating a sensing matrix based on the Taylor series expansion; and

determining the plurality of Taylor series coefficients based on the composite channel frequency response and the sensing matrix using compressive sensing channel estimation.

2. The method of claim 1 further comprising generating an estimated channel response based on the plurality of Taylor series coefficients.

3. The method of claim 1 wherein the channel impulse response is determined over L symbols.

4. The method of claim 3 wherein the channel frequency response is determined over the L symbols.

5. The method of claim 1 wherein the channel frequency response is determined using a discrete Fourier transform (DFT).

6. The method of claim 1 wherein the channel frequency response is determined using a fast Fourier transform (FFT).

7. The method of claim 2 wherein the sensing matrix is based on a set of Fourier coefficients.

8. The method of claim 2 wherein the compressive sensing channel estimation is based on a L1 norm minimization of the plurality of Taylor series coefficients subject to the constraint that g=U_sensing α

which is evaluated at a plurality of pilot locations, wherein g is the composite channel frequency response, U_sensing is the sensing matrix U_sensing and α

is the plurality of Taylor series coefficients.

9. The method of claim 8 wherein the L1 norm minimization is based on an absolute value minimization.

10. The method of claim 9 wherein the L1 norm minimization is based on a convex L1 norm minimization.

11. An apparatus for channel estimation comprising:

means for determining a channel impulse response using a Taylor series expansion with a plurality of Taylor series coefficients;

means for determining a channel frequency response based on the channel impulse response;

means for collecting the channel frequency response over a plurality of symbols to obtain a composite channel frequency response;

means for generating a sensing matrix based on the Taylor series expansion; and

means for determining the plurality of Taylor series coefficients based on the composite channel frequency response and the sensing matrix using compressive sensing channel estimation.

12. The apparatus of claim 11 further comprising means for generating an estimated channel response based on the plurality of Taylor series coefficients.

13. The apparatus of claim 11 wherein the channel impulse response is determined over L symbols.

14. The apparatus of claim 13 wherein the channel frequency response is determined over the L symbols.

15. The apparatus of claim 11 wherein the channel frequency response is determined using a discrete Fourier transform (DFT).

16. The apparatus of claim 11 wherein the channel frequency response is determined using a fast Fourier transform (FFT).

17. The apparatus of claim 12 wherein the sensing matrix is based on a set of Fourier coefficients.

18. The apparatus of claim 12 wherein the compressive sensing channel estimation is based on a L1 norm minimization of the plurality of Taylor series coefficients subject to the constraint that g=U_sensing α

which is evaluated at a plurality of pilot locations, wherein g is the composite channel frequency response, U_sensing is the sensing matrix U_sensing and α

is the plurality of Taylor series coefficients.

19. The apparatus of claim 18 wherein the L1 norm minimization is based on an absolute value minimization.

20. The apparatus of claim 19 wherein the L1 norm minimization is based on a convex L1 norm minimization.

21. An apparatus for channel estimation comprising a processor and a memory, the memory containing program code executable by the processor for performing the following:

determining a channel impulse response using a Taylor series expansion with a plurality of Taylor series coefficients;

determining a channel frequency response based on the channel impulse response;

collecting the channel frequency response over a plurality of symbols to obtain a composite channel frequency response;

generating a sensing matrix based on the Taylor series expansion; and

determining the plurality of Taylor series coefficients based on the composite channel frequency response and the sensing matrix using compressive sensing channel estimation.

22. The apparatus of claim 21 wherein the memory further comprising program code for generating an estimated channel response based on the plurality of Taylor series coefficients.

23. The apparatus of claim 21 wherein the channel impulse response is determined over L symbols.

24. The apparatus of claim 23 wherein the channel frequency response is determined over the L symbols.

25. The apparatus of claim 21 wherein the channel frequency response is determined using a discrete Fourier transform (DFT).

26. The apparatus of claim 21 wherein the channel frequency response is determined using a fast Fourier transform (FFT).

27. The apparatus of claim 22 wherein the sensing matrix is based on a set of Fourier coefficients.

28. The apparatus of claim 22 wherein the compressive sensing channel estimation is based on a L1 norm minimization of the plurality of Taylor series coefficients subject to the constraint that g=U_sensing α

which is evaluated at a plurality of pilot locations, wherein g is the composite channel frequency response, U_sensing is the sensing matrix U_sensing and α

is the plurality of Taylor series coefficients.

29. The apparatus of claim 28 wherein the L1 norm minimization is based on an absolute value minimization.

30. The apparatus of claim 29 wherein the L1 norm minimization is based on a convex L1 norm minimization.

31. A non-transitory computer-readable medium for channel estimation, the computer-readable medium storing a computer program, wherein execution of the computer program is for:

determining a channel impulse response using a Taylor series expansion with a plurality of Taylor series coefficients;

determining a channel frequency response based on the channel impulse response;

collecting the channel frequency response over a plurality of symbols to obtain a composite channel frequency response;

generating a sensing matrix based on the Taylor series expansion; and

determining the plurality of Taylor series coefficients based on the composite channel frequency response and the sensing matrix using compressive sensing channel estimation.

32. The non-transitory computer-readable medium of claim 31 wherein execution of the computer program is also for generating an estimated channel response based on the plurality of Taylor series coefficients.

33. The non-transitory computer-readable medium of claim 31 wherein the channel impulse response is determined over L symbols.

34. The non-transitory computer-readable medium of claim 33 wherein the channel frequency response is determined over the L symbols.

35. The non-transitory computer-readable medium of claim 31 wherein the channel frequency response is determined using a discrete Fourier transform (DFT).

36. The non-transitory computer-readable medium of claim 31 wherein the channel frequency response is determined using a fast Fourier transform (FFT).

37. The non-transitory computer-readable medium of claim 32 wherein the sensing matrix is based on a set of Fourier coefficients.

38. The non-transitory computer-readable medium of claim 32 wherein the compressive sensing channel estimation is based on a L1 norm minimization of the plurality of Taylor series coefficients subject to the constraint that g=U_sensing α

which is evaluated at a plurality of pilot locations, wherein g is the composite channel frequency response, U_sensing is the sensing matrix U_sensing and α

is the plurality of Taylor series coefficients.

39. The non-transitory computer-readable medium of claim 38 wherein the L1 norm minimization is based on an absolute value minimization.

40. The non-transitory computer-readable medium of claim 39 wherein the L1 norm minimization is based on a convex L1 norm minimization.