Demapper for rotated QAM constellations
A method includes receiving a symbol modulated with multiple bits according to a signal constellation including multiple constellation points. A soft metric is computed for a given bit in the symbol: A first constellation point closest to the received symbol according to a distance measure is found. A row or column of the constellation points, which is closest to the first constellation point according to the distance measure, and over which a value of the given bit is constant and is opposite to the value of the given bit in the first constellation point, is identified. At least the identified row or column is searched for a second constellation point that is closest to the received symbol according to the distance measure. The soft metric is calculated based on the first and second constellation points. The value of the given bit is reconstructed based on the soft metric.
1. A method, comprising:
receiving a symbol that has been modulated with multiple bits in accordance with a signal constellation comprising multiple constellation points;
computing a soft metric for a given bit in the received symbol by:
finding a first constellation point that is closest to the received symbol in accordance with a distance measure;
identifying a row or column of the constellation points that is closest to the first constellation point in accordance with the distance measure, and over which a value of the given bit is constant and is opposite to the value of the given bit in the first constellation point;
searching over at least the identified row or column for a second constellation point that is closest to the received symbol in accordance with the distance measure; and
calculating the soft metric based on the first and second constellation points; and
reconstructing the value of the given bit in the received symbol based on the soft metric.
2. The method according to claim 1 , wherein searching for the second constellation point comprises searching over the identified row or column and over an additional partial subset of the constellation points that is predefined for the first constellation point.
3. The method according to claim 2 , wherein searching for the second constellation point comprises accessing a Look-Up Table (LUT), which specifies a respective partial subset of the constellation points for each constellation point, so as to select the additional partial subset of the constellation points.
4. The method according to claim 1 , wherein the signal constellation comprises rows and columns of the constellation that are not parallel to respective signal space axes.
5. The method according to claim 1 , wherein calculating the soft metric comprises calculating a difference or a ratio between respective distances of the first and second constellation points from the received symbol.
6. The method according to claim 1 , wherein calculating the soft metric comprises conditionally inverting the soft metric based on a sign of the given bit in the first constellation point.
7. The method according to claim 1 , wherein searching for the second constellation point comprises deciding whether to search only over the identified row or column, or over the identified row or column and an additional predefined subset of the constellation points, based on a Signal to Noise Ratio (SNR) estimate.
8. The method according to claim 1 , wherein the distance measure comprises a Max-Log approximation of a Maximum Likelihood (ML) estimate.
9. Apparatus, comprising:
a front-end receiver, which is configured to receive a symbol that has been modulated with multiple bits in accordance with a signal constellation comprising multiple constellation points; and
a baseband processor, which is configured, for a given bit in the received symbol, to find a first constellation point that is closest to the received symbol in accordance with a distance measure, to identify a row or column of the constellation points that is closest to the first constellation point in accordance with the distance measure, and over which a value of the given bit is constant and is opposite to the value of the given bit in the first constellation point, to search over at least the identified row or column for a second constellation point that is closest to the received symbol in accordance with the distance measure, to compute the soft metric based on the first and second constellation points, and to reconstruct the value of the given bit in the received symbol based on the soft metric.
10. The apparatus according to claim 9 , wherein the baseband processor is configured to search for the second constellation point over the identified row or column and over an additional partial subset of the constellation points that is predefined for the first constellation point.
11. The apparatus according to claim 10 , and comprising a Look-Up Table (LUT) that specifies a respective partial subset of the constellation points for each constellation point, wherein the baseband processor is configured to access the LUT so as to select the additional partial subset of the constellation points.
12. The apparatus according to claim 9 , wherein the signal constellation comprises rows and columns of the constellation that are not parallel to respective signal space axes.
13. The apparatus according to claim 9 , wherein the baseband processor is configured to compute the soft metric by calculating a difference or a ratio between respective distances of the first and second constellation points from the received symbol.
14. The apparatus according to claim 9 , wherein the baseband processor is configured to conditionally invert the soft metric based on a sign of the given bit in the first constellation point.
15. The apparatus according to claim 9 , wherein the baseband processor is configured to decide whether to search only over the identified row or column, or over the identified row or column and an additional predefined subset of the constellation points, based on a Signal to Noise Ratio (SNR) estimate.
16. The apparatus according to claim 9 , wherein the distance measure comprises a Max-Log approximation of a Maximum Likelihood (ML) estimate.
17. A method, comprising:
receiving a symbol that has been modulated with multiple bits in accordance with a signal constellation comprising multiple constellation points;
computing a soft metric for a given bit in the received symbol by:
finding a first constellation point that is closest to the received symbol in accordance with a distance measure;
storing a first distance between the first constellation and the received symbol to serve as a term of the soft metric;
finding a second constellation point for which a value of the given bit is opposite from the value of the given bit in the first constellation point;
storing a second distance between the second constellation and the received symbol to serve as an opposite term of the soft metric; and
conditionally inverting the soft metric based on a sign of the given bit in the first constellation point; and
reconstructing the value of the given bit in the received symbol based on the soft metric.
18. The method according to claim 17 , wherein finding the second constellation point comprises searching over at least a row or column of the constellation points that is closest to the first constellation point in accordance with the distance measure.
19. Apparatus, comprising:
a front-end receiver, which is configured to receive a symbol that has been modulated with multiple bits in accordance with a signal constellation comprising multiple constellation points; and
a baseband processor, which is configured, for a given bit in the received symbol, to find a first constellation point that is closest to the received symbol in accordance with a distance measure, to store a first distance between the first constellation and the received symbol to serve as a term of a soft metric for the given bit, to find a second constellation point for which a value of the given bit is opposite from the value of the given bit in the first constellation point, to store a second distance between the second constellation and the received symbol to serve as an opposite term of the soft metric, to conditionally invert the soft metric based on a sign of the given bit in the first constellation point, and to reconstruct the value of the given bit in the received symbol based on the soft metric.
20. The apparatus according to claim 19 , wherein the baseband processor is configured to finding the second constellation point by searching over at least a row or column of the constellation points that is closest to the first constellation point in accordance with the distance measure.