Low complexity distance metrics for maximum likelihood receivers

• US 8,675,783 B1
• Filed: 12/02/2011
• Issued: 03/18/2014
• Est. Priority Date: 12/02/2010
• Status: Expired due to Fees

• Current Assignee: Marvell International Limited (Marvell Technology Group Limited)
• Original Assignee: Marvell International Limited (Marvell Technology Group Limited)
• Inventors: Song, Leilei, Nallapureddy, Bhaskar V., Lou, Hui-Ling, Matache, Adina
• Primary Examiner(s): Fan, Chieh M
• Assistant Examiner(s): Koeth, Michelle M
• Application Number:
  US13/309,684
• Time in Patent Office: 837 Days
• Field of Search: 375/341, 375/267, 375/340, 375/260, 714/780
• US Class Current: 375/341
• CPC Class Codes: H03M 13/45 Soft decoding, i.e. using symbol reliability information H03M13/41 takes precedence
• CPC Class Codes: H04L 1/0054 Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms
• CPC Class Codes: H04L 25/03171 Arrangements involving maximum a posteriori probability [MAP] detection
• CPC Class Codes: H04L 25/03242 Methods involving sphere decoding
• CPC Class Codes: H04L 25/03318 Provision of soft decisions

Abstract

Systems and methods are provided for determining a data value for a bit of interest in a received data signal. A closest 0-bit symbol candidate is selected from a plurality of 0-bit symbol candidates using a symbol selection distance approximation. A closest 1-bit symbol candidate is selected from a plurality of 1-bit symbol candidates using the symbol selection distance approximation. A 0-bit distance between the received data signal and the selected 0-bit symbol candidate is determined, and a 1-bit distance between the received data signal and the selected 1-bit symbol candidate is determined. A log likelihood ratio is calculated for the bit of interest using the determined 0-bit distance and the determined 1-bit distance.

Claims

1. A method of determining a data value for a bit of interest in a received data signal, the method comprising:

selecting a closest 0-bit symbol candidate, at the bit of interest, from a plurality of 0-bit symbol candidates using a symbol selection distance approximation;

selecting a closest 1-bit symbol candidate, at the bit of interest, from a plurality of 1-bit symbol candidates using the symbol selection distance approximation;

calculating a 0-bit distance and a 1-bit distance, wherein the 0-bit distance represents the distance between the received data signal and the selected closest 0-bit symbol candidate, and the 1-bit distance represents the distance between the received data signal and the selected closest 1-bit symbol candidate;

calculating a log likelihood ratio for the bit of interest using i) the calculated 0-bit distance and ii) the calculated 1-bit distance; and

determining the data value for the bit of interest based on the calculated log likelihood ratio;

wherein locations of each of the received data signal, the plurality of 0-bit symbol candidates, and the plurality of 1-bit symbol candidates are identified by coordinates;

wherein the symbol selection distance approximation, as applied to selecting the closest 0-bit symbol candidate, includes

estimating first distances between the received data signal and the plurality of 0-bit symbol candidates using norm approximations of vectors from the coordinates of the received data signal to coordinates of the plurality of 0-bit symbol candidates,

wherein the symbol selection distance approximation, as applied to selecting the closest 1-bit symbol candidate, includes

estimating second distances between the received data signal and the plurality of 1-bit symbol candidates using norm approximations of vectors from the coordinates of the received data signal to coordinates of the plurality of 1-bit symbol candidates,

wherein the vector between the coordinates of the received data signal and the coordinates of a 0-bit or 1-bit symbol candidate is represented as z_k=z_kI+jz_kQ,

wherein the norm approximation of ∥

z_k∥

estimates ∥

z_k∥

=max{|z_kI|,|z_kQ|}+α

·

min{|z_kI|,|z_kQ|}, where α

is 5/16, and

wherein the first or second distances are calculated according to a non-iterative distance approximation according to;

∥

z∥

≈

G(z),

where

3. The method of claim 1, wherein the plurality of 0-bit symbol candidates are symbols having a 0 value for the bit of interest, and wherein the plurality of 1-bit symbol candidates are symbols having a 1 value for the bit of interest.

4. The method of claim 1, wherein selecting a closest 0-bit symbol candidate includes:

determining the first distances between the received data signal and each of the plurality of 0-bit symbol candidates, wherein the first distances are determined using the symbol selection distance approximation; and

selecting one of the 0-bit symbol candidates based on the determined first distances.

5. The method of claim 1, wherein selecting a closest 1-bit symbol candidate includes:

determining the second distances between the received data signal and each of the plurality of 1-bit symbol candidates, wherein the second distances are determined using the symbol selection distance approximation; and

selecting one of the 1-bit symbol candidates based on the determined second distances.

6. The method of claim 1, wherein the 0-bit distance and the 1-bit distance are calculated using the symbol selection distance approximation.

7. The method of claim 1, wherein the 0-bit distance and the 1-bit distance are further calculated using a second distance approximation that is different from the symbol selection distance approximation.

8. The method of claim 1, wherein the 0-bit distance and the 1-bit distance are calculated using a squared Euclidean distance calculation.

9. The method of claim 1, wherein the symbol selection distance approximation uses an iterative distance approximation or a non-iterative distance approximation;

and

wherein the 0-bit distance or the 1-bit distance are calculated using the iterative distance approximation, the non-iterative distance approximation, or a squared Euclidean distance calculation.

10. The method of claim 9, wherein the squared Euclidean distance calculation calculates a distance for a complex vector of dimension N according to:

∥

z∥

²=Σ

_k=1^N|z_kI|²+Σ

_k=1^N|z_kQ|².

11. The method of claim 1, wherein the first distances between the received data signal and the plurality of 0-bit symbol candidates are used to select the 0-bit symbol candidate that fulfills

12. The method of claim 11, wherein the log likelihood ratio is calculated according to:

L(b_k⁽ⁱ⁾)≈

1/σ

²{||y−

Hx₀||²−

||y−

Hx₁||²},

where ∥

y−

Hx₀∥

is the 0-bit distance, |y−

Hx₁∥

is the 1-bit distance, L(b_k⁽ⁱ⁾) is the log likelihood ratio for a bit of interest, and σ

² is a variance of noise.

13. The method of claim 12, wherein the bit of interest is determined to be as 0 or a 1 based on the log likelihood ratio.

14. The method of claim 1, wherein the received data signal is a multiple input, multiple output (MIMO) signal.

15. The method of claim 1, wherein the received data signal is a single carrier signal.

2. A method of determining a data value for a bit of interest in a received data signal, the method comprising:

selecting a closest 0-bit symbol candidate, at the bit of interest, from a plurality of 0-bit symbol candidates using a symbol selection distance approximation;

selecting a closest 1-bit symbol candidate, at the bit of interest, from a plurality of 1-bit symbol candidates using the symbol selection distance approximation;

calculating a 0-bit distance and a 1-bit distance, wherein the 0-bit distance represents the distance between the received data signal and the selected closest 0-bit symbol candidate, and the 1-bit distance represents the distance between the received data signal and the selected closest 1-bit symbol candidate;

calculating a log likelihood ratio for the bit of interest using i) the calculated 0-bit distance and ii) the calculated 1-bit distance; and

determining the data value for the bit of interest based on the calculated log likelihood ratio;

wherein locations of each of the received data signal, the plurality of 0-bit symbol candidates, and the plurality of 1-bit symbol candidates are identified by coordinates;

wherein the symbol selection distance approximation, as applied to selecting the closest 0-bit symbol candidate, includes

estimating first distances between the received data signal and the plurality of 0-bit symbol candidates using norm approximations of vectors from the coordinates of the received data signal to coordinates of the plurality of 0-bit symbol candidates,

wherein the symbol selection distance approximation, as applied to selecting the closest 1-bit symbol candidate, includes

estimating second distances between the received data signal and the plurality of 1-bit symbol candidates using norm approximations of vectors from the coordinates of the received data signal to coordinates of the plurality of 1-bit symbol candidates,

wherein the vector between the coordinates of the received data signal and the coordinates of a 0-bit or 1-bit symbol candidate is represented as z_k=z_kI+jz_kQ,

wherein the norm approximation of ∥

z_k∥

estimates ∥

z_k∥

=max{|z_kI|,|z_kQ|}+α

·

min{∥

z_kI|,|z_kQ|}, where α

is 5/16, and

wherein the first or second distances are calculated according to an iterative distance approximation according to;

∥

z∥

≈

{hacek over (G)}(z)^(N),

where

{hacek over (G)}(z)⁽¹⁾=g(z₁),

where

{hacek over (G)}(z)^(k)=max{g(z_k),G(z)<sup>(k−

1)</sup>}+α

·

min{g(z_k),G(z)<sup>(k−

1)</sup>}, k=2 . . . N,

where

g(z_k)=max{|z_kI|,|z_kQ|}+α

·

min{|z_kI|,|z_kQ|}, k=1 . . . N.

16. The method of claim 2, wherein the plurality of 0-bit symbol candidates are symbols having a 0 value for the bit of interest, and wherein the plurality of 1-bit symbol candidates are symbols having a 1 value for the bit of interest.

17. The method of claim 2, wherein selecting a closest 0-bit symbol candidate includes:

determining the first distances between the received data signal and each of the plurality of 0-bit symbol candidates, wherein the first distances are determined using the symbol selection distance approximation; and

selecting one of the 0-bit symbol candidates based on the determined first distances.

18. The method of claim 2, wherein selecting a closest 1-bit symbol candidate includes:

determining the second distances between the received data signal and each of the plurality of 1-bit symbol candidates, wherein the second distances are determined using the symbol selection distance approximation; and

selecting one of the 1-bit symbol candidates based on the determined second distances.

19. The method of claim 2, wherein the 0-bit distance and the 1-bit distance are calculated using the symbol selection distance approximation.

20. The method of claim 2, wherein the 0-bit distance and the 1-bit distance are further calculated using a second distance approximation that is different from the symbol selection distance approximation.

21. The method of claim 2, wherein the 0-bit distance and the 1-bit distance are calculated using a squared Euclidean distance calculation.

22. The method of claim 2, wherein the symbol selection distance approximation uses an iterative distance approximation or a non-iterative distance approximation;

and

wherein the 0-bit distance or the 1-bit distance are calculated using the iterative distance approximation, the non-iterative distance approximation, or a squared Euclidean distance calculation.

23. The method of claim 22, wherein the squared Euclidean distance calculation calculates a distance for a complex vector of dimension N according to:

∥

z∥

²=Σ

_k=1^N|z_kI|²+Σ

_k=1^N|z_kQ|².

24. The method of claim 2, wherein the first distances between the received data signal and the plurality of 0-bit symbol candidates are used to select the 0-bit symbol candidate that fulfills

25. The method of claim 24, wherein the log likelihood ratio is calculated according to:

L(b_k⁽ⁱ⁾)≈

1/σ

²{||y−

Hx₀||²−

||y−

Hx₁||²},

where ∥

y−

Hx₀∥

is the 0-bit distance, |y−

Hx₁∥

is the 1-bit distance, L(b_k⁽ⁱ⁾) is the log likelihood ratio for a bit of interest, and σ

² is a variance of noise.

26. The method of claim 25, wherein the bit of interest is determined to be a 0 or a 1 based on the log likelihood ratio.

27. The method of claim 2, wherein the received data signal is a multiple input, multiple output (MIMO) signal.

28. The method of claim 2, wherein the received data signal is a single carrier signal.