Joint equalization, soft-demapping and phase error correction in wireless system with receive diversity

• US 20030123582A1
• Filed: 05/06/2002
• Published: 07/03/2003
• Est. Priority Date: 12/27/2001
• Status: Active Grant

• Current Assignee: DSP Group Incorporated (Synaptics Incorporated)
• Original Assignee: DSP Group Incorporated (Synaptics Incorporated)
• Inventors: Rad, Farshid R., Moon, Jaekyun, Kim, Younggyun, Brickner, Barrett J.
• Granted Patent: US 7,173,990 B2
• Time in Patent Office: Days
• US Class Current: 375/347
• CPC Class Codes: H04B 7/0837 using pre-detection combining H04B7/0868 takes precedence
• CPC Class Codes: H04B 7/0848 Joint weighting
• CPC Class Codes: H04L 1/06 using space diversity
• CPC Class Codes: H04L 2025/03414 Multicarrier
• CPC Class Codes: H04L 2025/0342 QAM
• CPC Class Codes: H04L 2025/03426 transmission using multiple-input and multiple-output channels
• CPC Class Codes: H04L 2027/003 at baseband only
• CPC Class Codes: H04L 2027/004 the equaliser providing control signals
• CPC Class Codes: H04L 2027/0057 quadrature phase
• CPC Class Codes: H04L 25/0204 of multiple channels
• CPC Class Codes: H04L 25/03159 operating in the frequency domain H04L25/03165, H04L25/03178 take precedence
• CPC Class Codes: H04L 25/067 providing soft decisions, i.e. decisions together with an estimate of reliability H04L25/068 and H04L25/069 take precedence; sequence estimation techniques H04L25/03178
• CPC Class Codes: H04L 27/38 Demodulator circuits; Receiver circuits

Abstract

A wireless communication technique enables equalization, soft demapping and phase error estimation functions to be performed jointly based on multiple observations of a transmitted symbol in wireless communication systems employing receive diversity. Multiple observations of a symbol are obtained from multiple antenna paths in a wireless receiver. Equalization, soft demapping and phase error estimation functions can be integrated within shared hardware, rather than distributed among separate hardware blocks, promoting reduced size, complexity and cost in a wireless receiver.

Claims

1. A method comprising:

receiving wireless signals via multiple antennas;

demodulating the wireless signals to produce observations of a transmitted symbol;

weighting each of the observations with a complex-conjugate of a channel response for the corresponding antenna;

combining the weighted observations to form a combined observation; and

generating one or more soft decision bits indicative of the transmitted symbol for the combined observation according to soft demapping rules based on a subset of the transmitted symbol constellation.

2. The method of claim 1, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a second minimum distance symbol associated with bit 0.

3. The method of claim 2, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

4. The method of claim 1, wherein the soft demapping rules are based on piecewise linear functions.

5. The method of claim 1, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

6. The method of claim 5, further comprising computing one or more of the soft decisions recursively based on previously computed soft decisions.

7. The method of any of claims 1 to 6, further comprising estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

8. The method of any of claims 1 to 6, wherein the wireless signals are multi-carrier (MC) signals, the method further comprising applying a Fourier transform function to obtain the observations of the transmitted symbol.

9. The method of claim 1, further comprising estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone, and performing the generation and estimation functions jointly within shared hardware.

10. A method comprising:

receiving orthogonal frequency division multiplexing (OFDM) wireless signals via multiple antennas;

demodulating and performing fast Fourier transform (FFT) functions on the wireless signals to produce observations of a transmitted quadrature amplitude modulated (QAM) symbol;

weighting each of the observations with a complex-conjugate of a channel response for the corresponding antenna;

combining the weighted observations to form a combined observation; and

generating one or more soft decision bits indicative of the transmitted QAM symbol for the combined observation according to soft demapping rules based on a subset of the transmitted QAM symbol constellation.

11. The method of claim 10, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a first minimum distance symbol associated with bit 0.

12. The method of claim 10, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

13. The method of claim 10, wherein the soft demapping rules are based on piecewise linear functions.

14. The method of claim 10, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

15. The method of claim 14, further comprising computing one or more of the soft decisions recursively based on previously computed soft decisions.

16. The method of any of claims 10 to 15, further comprising estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

17. The method of claim 10, further comprising:

estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone;

estimating the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error; and

estimating the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers.

18. The method of claim 17, further comprising:

adjusting an FFT sampling window for each of the wireless signals based on the sampling phase error; and

applying a frequency domain correction to subsequent observations based on the carrier phase error and sampling phase error.

19. The method of claim 17, further comprising applying a time domain correction to subsequent observations based on the carrier phase error and sampling phase error.

20. The method of claim 17, further comprising:

adjusting an FFT sampling window for each of the wireless signals based on the sampling phase error;

applying a time domain correction to subsequent observations based on the carrier phase error; and

applying a frequency domain correction to subsequent observations based on the sampling phase error.

21. The method of claim 17, further comprising performing the generation and estimation functions jointly within shared hardware.

22. The method of claim 17, wherein estimating the carrier phase error includes summing the estimated combined phase errors that correspond to multiple pairs of complementary subcarriers, and averaging the resulting sums.

23. The method of claim 22, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of an estimated combined signal-to-noise ratio for the antennas and an estimated power of the transmitted symbol.

24. The method of claim 22, further comprising selecting subcarriers having energy levels above a threshold, and using the selected subcarriers to choose the pairs of complementary subcarriers used to estimate the carrier phase error.

25. The method of claim 17, wherein estimating the sampling phase error includes subtracting the estimated combined phase errors that correspond to multiple pairs of subcarriers, and averaging the resulting differences.

26. The method of claim 25, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of:

the estimated combined signal-to-noise ratio for the antennas or the estimated power of the transmitted symbol.

27. The method of claim 25, further comprising selecting subcarriers having energy levels above a threshold, and using the selected subcarriers to choose the pairs of subcarriers used to estimate the sampling phase error.

28. The method of any of claims 10 to 15, wherein the wireless signals are transmitted according to the IEEE 802.11a standard.

29. A method comprising:

receiving an orthogonal frequency division multiplexing (OFDM) wireless signal via a first antenna;

receiving the orthogonal frequency division multiplexing (OFDM) wireless signal via a second antenna;

demodulating and performing fast Fourier transform (FFT) functions on the wireless signal received by the first antenna to produce a first observation of a transmitted quadrature amplitude modulated (QAM) symbol;

demodulating and performing fast Fourier transform (FFT) functions on the wireless signal received by the second antenna to produce a second observation of the transmitted quadrature amplitude modulated (QAM) symbol;

weighting the first observation with a complex-conjugate of a channel response for the first antenna;

weighting the second observation with a complex-conjugate of a channel response for the second antenna;

combining the weighted first observation and the weighted second observation to form a combined observation; and

generating one or more soft decision bits indicative of the transmitted QAM symbol for the combined observation according to soft demapping rules based on a subset of the transmitted QAM symbol constellation.

30. The method of claim 29, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a first minimum distance symbol associated with bit 0.

31. The method of claim 29, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

32. The method of claim 29, wherein the soft demapping rules are based on piecewise linear functions.

33. The method of claim 29, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

34. The method of claim 33, further comprising computing one or more of the soft decisions recursively based on previously computed soft decisions.

35. The method of any of claims 29-34, further comprising:

estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone;

estimating the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error; and

estimating the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers.

36. The method of claim 29, further comprising:

estimating a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone;

estimating the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error;

estimating the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers;

adjusting an FFT sampling window for each of the wireless signals based on the sampling phase error; and

applying a frequency domain correction to subsequent observations based on the carrier phase error and sampling phase error.

37. The method of claim 36, further comprising applying a time domain correction to subsequent observations based on the carrier phase error and sampling phase error.

38. The method of claim 36, further comprising:

adjusting an FFT sampling window for each of the wireless signals based on the sampling phase error;

applying a time domain correction to subsequent observations based on the carrier phase error; and

applying a frequency domain correction to subsequent observations based on the sampling phase error.

39. The method of claim 36, further comprising performing the generation and estimation functions jointly within shared hardware.

40. The method of claim 36, wherein estimating the carrier phase error includes summing the estimated combined phase errors that correspond to multiple pairs of complementary subcarriers, and averaging the resulting sums.

41. The method of claim 40, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of an estimated combined signal-to-noise ratio for the antennas and an estimated power of the transmitted symbol.

42. The method of claim 40, further comprising selecting subcarriers having energy levels above a threshold, and using the selected subcarriers to choose the pairs of complementary subcarriers used to estimate the carrier phase error.

43. The method of claim 36, wherein estimating the sampling phase error includes subtracting the estimated combined phase errors that correspond to multiple pairs of subcarriers, and averaging the resulting differences.

44. The method of claim 43, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of:

the estimated combined signal-to-noise ratio for the antennas or the estimated power of the transmitted symbol.

45. The method of claim 36, further comprising selecting subcarriers having energy levels above a threshold, and using the selected subcarriers to choose the pairs of subcarriers used to estimate the sampling phase error.

46. The method of any of claims 29 to 34, wherein the wireless signals are transmitted according to the IEEE 802.11a standard.

47. A method comprising:

receiving an orthogonal frequency division multiplexing (OFDM) wireless signal via an antenna;

demodulating and performing a fast Fourier transform (FFT) function on the wireless signal to produce an observation of a transmitted quadrature amplitude modulated (QAM) symbol;

weighting the observation with a complex-conjugate of a channel response for the antenna; and

generating one or more soft decision bits indicative of the transmitted symbol for the weighted observation according to soft demapping rules based on a subset of the transmitted symbol constellation.

48. The method of claim 47, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a second minimum distance symbol associated with bit 0.

49. The method of claim 47, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

50. The method of claim 47, wherein the soft demapping rules are based on piecewise linear functions.

51. The method of claim 47, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the weighted observation and the energy of the channel response.

52. The method of claim 51, further comprising computing one or more of the soft decisions recursively based on previously computed soft decisions.

53. The method of any of claims 47 to 52, further comprising:

estimating a combined phase error including carrier phase error and sampling phase error for the weighted observation using one of the transmitted symbol estimated based on the soft decision bits or a predetermined symbol transmitted via a pilot tone;

estimating the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error; and

estimating the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers.

54. The method of claim 47, further comprising:

estimating a combined phase error including carrier phase error and sampling phase error for the weighted observation using one of the transmitted symbol estimated based on the soft decision bits or a predetermined symbol transmitted via a pilot tone;

estimating the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error;

estimating the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers;

adjusting an FFT sampling window for the wireless signal based on the sampling phase error; and

applying a frequency domain correction to subsequent observations based on the carrier phase error and sampling phase error.

55. The method of claim 54, further comprising applying a time domain correction to subsequent observations based on the carrier phase error and sampling phase error.

56. The method of claim 54, further comprising:

adjusting an FFT sampling window for the wireless signal based on the sampling phase error;

applying a time domain correction to subsequent observations based on the carrier phase error; and

applying a frequency domain correction to subsequent observations based on the sampling phase error.

57. The method of claim 54, further comprising performing the generation and estimation functions jointly within shared hardware.

58. The method of any of claims 47 to 52, wherein the wireless signal is transmitted according to the IEEE 802.11a standard.

59. A wireless receiver comprising:

multiple antennas that receive wireless signals;

a demodulator that demodulates the wireless signals to produce observations of a transmitted symbol;

an equalizer that weights each of the observations with a complex conjugate of an estimated channel response for the corresponding antenna; and

a soft demapper unit that combines the weighted observations to form a combined observation, and generates one or more soft decision bits indicative of the transmitted symbol for the combined observation according to soft demapping rules based on a subset of the transmitted symbol constellation.

60. The receiver of claim 59, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a first minimum distance symbol associated with bit 0.

61. The receiver of claim 60, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

62. The receiver of claim 59, wherein the soft demapping rules are based on piecewise linear functions.

63. The receiver of claim 59, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

64. The receiver of claim 63, wherein the soft demapper unit computes one or more of the soft decisions recursively based on previously computed soft decisions.

65. The receiver of any of claims 59 to 64, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

66. The receiver of claim 59, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone, wherein the soft demapper unit and the phase error estimator are provided jointly within shared hardware.

67. The receiver of any of claims 59 to 64, wherein the wireless signals are multi-carrier (MC) signals, the receiver further comprising applying a Fourier transform function to obtain the observations of the transmitted symbol.

68. A receiver comprising:

multiple antennas that receive orthogonal frequency division multiplexing (OFDM) wireless signals via multiple antennas;

a fast Fourier transform (FFT) unit that produce observations of a transmitted quadrature amplitude modulated (QAM) symbol from the wireless signals;

an equalizer that weights each of the observations with a complex-conjugate of a channel response for the corresponding antenna; and

a soft demapper unit that combines the weighted observations to form a combined observation, and generates one or more soft decision bits indicative of the transmitted QAM symbol for the combined observation according to soft demapping rules based on a subset of the transmitted QAM symbol constellation.

69. The receiver of claim 68, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a first minimum distance symbol associated with bit 0.

70. The receiver of claim 68, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

71. The receiver of claim 68, wherein the soft demapping rules are based on piecewise linear functions.

72. The receiver of claim 68, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

73. The receiver of claim 72, wherein the soft demapper unit computes one or more of the soft decisions recursively based on previously computed soft decisions.

74. The receiver of any of claims 68 to 73, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

75. The receiver of claim 68, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone, wherein the phase error estimator estimates the carrier phase error by summing the estimated combined phase errors that correspond to complementary subcarriers in the wireless signals to remove the sampling phase error, and estimates the sampling phase error by subtracting the estimated combined phase error that corresponds to one of the subcarriers from the estimated combined phase error that corresponds to another of the subcarriers.

76. The receiver of claim 75, further comprising a phase error adjusting unit that adjusts an FFT sampling window for each of the wireless signals based on the sampling phase error, and applies a frequency domain correction to subsequent observations based on the carrier phase error and sampling phase error.

77. The receiver of claim 75, further comprising a phase error adjusting unit that applies a time domain correction to subsequent observations based on the carrier phase error and the sampling phase error.

78. The receiver of claim 75, further comprising a phase error adjusting unit that adjusts an FFT sampling window for each of the wireless signals based on the sampling phase error, applies a time domain correction to subsequent observations based on the carrier phase error, and applies a frequency domain correction to subsequent observations based on the sampling phase error.

79. The receiver of claim 75, wherein the soft demapper unit and the phase error estimator are provided jointly within shared hardware.

80. The receiver of claim 75, wherein the phase error estimator estimates the carrier phase error by summing the estimated combined phase errors that correspond to multiple pairs of complementary subcarriers, and averaging the resulting sums.

81. The receiver of claim 80, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of an estimated combined signal-to-noise ratio for the antennas and an estimated power of the transmitted symbol.

82. The receiver of claim 80, wherein the phase error estimator selects subcarriers having energy levels above a threshold, and uses the selected subcarriers to choose the pairs of complementary subcarriers used to estimate the carrier phase error.

83. The receiver of claim 75, wherein the phase error estimator estimates the sampling phase error by subtracting the estimated combined phase errors that correspond to multiple pairs of subcarriers, and averaging the resulting differences.

84. The receiver of claim 83, wherein averaging includes weighting each of the estimated combined phase errors according to at least one of the estimated combined signal-to-noise ratio for the antennas or the estimated power of the transmitted symbol.

85. The receiver of claim 83, wherein the phase error estimator selects subcarriers having energy levels above a threshold, and uses the selected subcarriers to choose the pairs of subcarriers used to estimate the sampling phase error.

86. The receiver of any of claims 68 to 73, wherein the wireless signals are transmitted according to the IEEE 802.11a standard.

87. A receiver comprising:

a first antenna that receives an orthogonal frequency division multiplexing (OFDM) wireless signal;

a second antenna that receives the orthogonal frequency division multiplexing (OFDM) wireless signal;

a first fast Fourier transform (FFT) unit that produces a first observation of a transmitted quadrature amplitude modulated (QAM) symbol from the wireless signal received by the first antenna;

a second fast Fourier transform (FFT) unit that produces a second observation of a transmitted quadrature amplitude modulated (QAM) symbol from the wireless signal received by the second antenna;

an equalizer that weights the first observation with a complex-conjugate of a channel response for the first antenna, and weights the second observation with a complex-conjugate of a channel response for the second antenna;

a soft demapper unit that combines the weighted first observation and the weighted second observation to form a combined observation, and generates one or more soft decision bits indicative of the transmitted QAM symbol for the combined observation according to soft demapping rules based on a subset of the transmitted QAM symbol constellation.

88. The receiver of claim 87, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a first minimum distance symbol associated with bit 0.

89. The receiver of claim 87, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

90. The receiver of claim 87, wherein the soft demapping rules are based on piecewise linear functions.

91. The receiver of claim 87, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

92. The receiver of claim 91, wherein the soft demapper unit computes one or more of the soft decisions recursively based on previously computed soft decisions.

93. The receiver of any of claims 87-92, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the combined observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

94. A receiver comprising:

an antenna that receives an orthogonal frequency division multiplexing (OFDM) wireless signal;

a fast Fourier transform (FFT) function unit that produces an observation of a transmitted quadrature amplitude modulated (QAM) symbol from the wireless signal;

an equalizer that weights the observation with a complex-conjugate of a channel response for the antenna; and

a soft demapper unit that generates one or more soft decision bits indicative of the transmitted symbol for the weighted observation according to soft demapping rules based on a subset of the transmitted symbol constellation.

95. The receiver of claim 94, wherein the soft demapping rules are based on a first minimum distance symbol associated with bit 1 and a second minimum distance symbol associated with bit 0.

96. The receiver of claim 94, wherein the minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

97. The receiver of claim 94, wherein the soft demapping rules are based on piecewise linear functions.

98. The receiver of claim 94, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the weighted observation and the energy of the channel response.

99. The receiver of claim 94, wherein the soft demapper unit computes one or more of the soft decisions recursively based on previously computed soft decisions.

100. The receiver of any of claims 94-99, further comprising a phase error estimator that estimates a combined phase error including carrier phase error and sampling phase error for the observation using one of the transmitted symbol estimated based on the soft decision bits and a predetermined symbol transmitted via a pilot tone.

101. A method comprising applying a soft decision function to generate soft decision bits for a combined transmitted symbol observation produced from wireless signals received via multiple receive paths, wherein the soft decision function defines soft demapping rules based on a subset of the transmitted symbol constellation.

102. The method of claim 101, wherein the soft demapping rules are based on a first minimum distance symbol associated with a first bit encoded in the transmitted symbol and a second minimum distance symbol associated with a second bit in the transmitted symbol.

103. The method of claim 102, wherein the first and second minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

104. The method of claim 101, further comprising receiving the wireless signals via multiple antennas, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

105. The method of claim 101, wherein the wireless signals are transmitted according to the IEEE 802.11a standard.

106. A receiver comprising a soft demapper unit that applies a soft decision function to generate soft decision bits for a combined QAM symbol produced from wireless signals received via multiple receive paths, wherein the soft decision function defines soft demapping rules based on a subset of the transmitted symbol constellation.

107. The receiver of claim 106, wherein the soft demapping rules are based on a first minimum distance symbol associated with a first bit encoded in the transmitted symbol and a second minimum distance symbol associated with a second bit in the transmitted symbol.

108. The receiver of claim 107, wherein the first and second minimum distance symbols are constrained to be within a predetermined distance of an inter-bit decision boundary.

109. The receiver of claim 106, further comprising receiving the wireless signals via multiple antennas, wherein the soft demapping rules are based on piecewise linear functions of real and imaginary components of the combined observation and a combined energy of the channel responses for the multiple antennas.

110. The receiver of claim 106, wherein the wireless signals are transmitted according to the IEEE 802.11a standard.