Coherent reception with noisy channel state information
Systems and methods for improved coherent demodulation that account for variation of an effective channel estimation error with transmitted symbols are provided. In one embodiment, a wireless node includes a receiver front-end, a channel estimator, and a soft-value processor. The receiver front-end is adapted to output samples of a received signal. The channel estimator is adapted to estimate a channel between a transmitter of the received signal and the wireless node based on the samples of the received signal. The soft-value processor is adapted to process the samples of the received signal according to a soft-value generation scheme that accounts for variation of an effective channel estimation error with transmitted symbols to thereby provide corresponding soft values. By accounting for the variation of the effective channel estimation error with transmitted symbols, the soft-value processor provides improved performance, particularly in a low Signal-to-Noise Ratio (SNR) scenario.
1. A wireless node comprising:
a Radio Frequency, RF, front-end adapted to output samples of a received signal;
a channel estimator adapted to estimate a channel between a transmitter of the received signal and the wireless node based on the samples of the received signal; and
a soft-value processor adapted to process the samples of the received signal according to a soft-value generation scheme that accounts for variation of effective channel estimation error with transmitted symbols to thereby provide corresponding soft values,
wherein the soft-value generation scheme is based on a modified maximum likelihood metric that accounts for the variation of the effective channel estimation error with transmitted symbols and wherein the modified maximum likelihood metric is defined as:
μ( s )=β( s ) −1 ∥r−ĥs∥ 2 +MN 0 ln β( s )
where μ(s) is the modified maximum likelihood metric for a symbol s, r is the received signal, ĥ is a channel estimate provided by the channel estimator, M is a number of receive antennas of the wireless node, N 0 is noise power spectral density, and β(s) is defined as:
β( s )=1+| s| 2 /G,
where G is a processing gain resulting from channel estimation.
2. The wireless node of claim 1 wherein a modulation scheme of the received signal has a modulation alphabet A containing 2 k symbols, and, in order to provide the soft values, the soft-value processor is adapted to, for each sample of the received signal:
select a symbol hypothesis s from the modulation alphabet A that minimizes the modified maximum likelihood metric μ({tilde over (s)}) for the sample of the received signal as a symbol decision ŝ representing bits {circumflex over (b)} 0 . . . {circumflex over (b)} k-1 ; and
for each bit {circumflex over (b)} 1 in {circumflex over (b)} 0 . . . {circumflex over (b)} k-1 , generate a soft value for bit {circumflex over (b)} i based on a difference between μ({hacek over (s)}) and μ(ŝ), where {hacek over (s)} is a symbol from a subset {hacek over (A)} of the modulation alphabet A containing all symbol hypotheses {tilde over (s)} having a bit value {hacek over (b)} i that is the opposite of the bit {circumflex over (b)} i that minimizes μ({tilde over (s)}) for the subset {hacek over (A)}.
3. The wireless node of claim 2 wherein the soft-value processor is further adapted to generate the soft value for the bit {circumflex over (b)} 1 according to:
δ( {circumflex over (b)} i )=μ({hacek over ( s )})−μ({circumflex over ( s )}),
where δ({circumflex over (b)} i ) is the soft value for the bit {circumflex over (b)} i .
4. The wireless node of claim 2 wherein the soft-value processor is further adapted to generate the soft value for the bit {circumflex over (b)} i according to:
δ( {circumflex over (b)} i )=(−1) {circumflex over (b)} i (μ({hacek over ( s )})−μ({circumflex over ( s )})),
where δ({circumflex over (b)} i ) is the soft value for the bit {circumflex over (b)} i and the soft value δ({circumflex over (b)} i ) represents both a bit decision for the bit {circumflex over (b)} i and a confidence of the bit decision for the bit {circumflex over (b)} i .
5. The wireless node of claim 1 wherein a modulation scheme of the received signal is a Gray-Mapped N Quadrature Amplitude Modulation, N-QAM, scheme having a modulation alphabet A containing 2 k =N symbols.
6. The wireless node of claim 5 wherein in order to provide the soft values, the soft-value processor is adapted to, for each sample of the received signal, generate a soft value for each bit {circumflex over (b)} i in b 0 . . . b k-1 of a corresponding received symbol utilizing less than N values of the modified maximum likelihood metric.
7. The wireless node of claim 5 wherein in order to provide the soft values, the soft-value processor is adapted to, for each sample of the received signal:
compute values of the modified maximum likelihood metric defined as:
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wherein a received symbol s(b 0 , b 1 , b 2 , b 3 ) is a function of bits b 0 . . . b 3 , μ(s(*,*, b 2 , b 3 )) is the modified maximum likelihood metric for the received symbol s(b 0 , b 1 , b 2 , b 3 ) minimized over all possible choices of the bits b 0 and b 1 for given values for the bits b 2 and b 3 , and x is defined as:
x √{square root over (2/5)} ĥ H r ; and
generate soft values for each bit b i in b 0 . . . b 3 of a corresponding received symbol based on values μ(s(*,*,0,0)), μ(s(*,*,0,1)), μ(s(*,*,1,0)), and μ(s(*,*,1,1)).
8. The wireless node of claim 7 wherein in order to generate the soft values for each bit b i in b 0 . . . b 3 of the corresponding received symbol, the soft-value processor is further adapted to:
generate the soft value δ(b 0 ) for the bit b 0 in b 0 . . . b 3 of the corresponding received symbol according to:
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generate the soft value δ(b 1 ) for the bit b 1 in b 0 . . . b 3 of the corresponding received symbol according to:
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;
generate the soft value δ(b 2 ) for the bit b 2 in b 0 . . . b 3 of the corresponding received symbol according to:
δ( b 2 )=μ( s (*,*,0,*))−μ( s (*,*,1,*)); and
generate the soft value δ(b 3 ) for the bit b 3 in b 0 . . . b 3 of the corresponding received symbol according to:
δ( b 3 )=μ( s (*,*,*,0))−μ( s (*,*,*,1,1));
wherein:
μ(s(*,*,0,*)) is defined as:
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μ(s(*,*,1,*)) is defined as:
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μ(s(*,*,*,*)) is defined as:
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.
9. The wireless node of claim 5 wherein in order to provide the soft values, the soft-value processor is adapted to, for each sample of the received signal:
compute values of the modified maximum likelihood metric for a corresponding received symbol s(b 0 , b 1 , b 2 , . . . , b k-1 ) minimized over all possible choices of bits b 0 and b 1 , where each value of the modified maximum likelihood metric corresponds to a different combination of values for bits b 2 through b k-1 ; and
generate soft values for each bit b 1 in b 0 , b 1 , b 2 , . . . , b k-1 of the corresponding received symbol s(b 0 , b 1 , b 2 , . . . , b k-1 ) based on the values of the modified maximum likelihood metric.
10. The wireless node of claim 1 wherein each sample of the received signal corresponds to a received symbol, and the soft-value processor is adapted to provide, for each bit of each received symbol, a bit decision for the bit and a soft value that represents a confidence of the bit decision.
11. The wireless node of claim 1 wherein each sample of the received signal corresponds to a received symbol, and the soft-value processor is adapted to provide a soft value for each bit of each received symbol that represents both a bit decision for the bit and a confidence of the bit decision.
12. A method of operation of a wireless node comprising:
providing samples of a received signal;
estimating a channel between a transmitter of the received signal and the wireless node based on the samples of the received signal; and
processing the samples of the received signal according to a soft-value generation scheme that accounts for variation of effective channel estimation error with transmitted symbols to thereby provide corresponding soft values,
wherein the soft-value generation scheme is based on a modified maximum likelihood metric that accounts for the variation of the effective channel estimation error with transmitted symbols and wherein the modified maximum likelihood metric is defined as:
μ( s )=β( s ) −1 ∥r−{hacek over (h)}s∥ 2 +MN 0 ln β( s )
where μ(s) is the modified maximum likelihood metric for a symbol s, r is the received signal, ĥ is a channel estimate, M is a number of receive antennas of the wireless node, N 0 is noise power spectral density, and β(s) is defined as:
β( s )=1+| s| 2 /G,
where G is a processing gain resulting from channel estimation.
13. The method of claim 12 wherein a modulation scheme of the received signal has a modulation alphabet A containing 2 k symbols, and providing the soft values comprises, for each sample of the received signal:
selecting a symbol hypothesis {tilde over (s)} from the modulation alphabet A that minimizes the modified maximum likelihood metric μ({tilde over (s)}) for the sample of the received signal as a symbol decision ŝ representing bits {circumflex over (b)} 0 . . . {circumflex over (b)} k-1 ; and
for each bit {circumflex over (b)} i in {circumflex over (b)} 0 . . . {circumflex over (b)} k-1 , generating a soft value for bit {circumflex over (b)} i based on a difference between μ({hacek over (s)}) and μ(ŝ), where {hacek over (s)} is a symbol from a subset {hacek over (A)} of the modulation alphabet A containing all symbol hypotheses {tilde over (s)} having a bit value {hacek over (b)} i that is the opposite of the bit {circumflex over (b)} i that minimizes μ({tilde over (s)}) for the subset {hacek over (A)}.
14. The method of claim 13 wherein generating the soft value for the bit {circumflex over (b)} i comprises generating the soft value for the bit {circumflex over (b)} i according to:
δ( {circumflex over (b)} i )=μ({hacek over ( s )})−μ({circumflex over ( s )}),
where δ({circumflex over (b)} i ) is the soft value for the bit {circumflex over (b)} i .
15. The method of claim 13 wherein generating the soft value for the bit {circumflex over (b)} i comprises generating the soft value for the bit {circumflex over (b)} i according to:
δ( {circumflex over (b)} i )=(−1) {circumflex over (b)} i (μ({hacek over ( s )})−μ({circumflex over ( s )})),
where δ({circumflex over (b)} i ) is the soft value for the bit {circumflex over (b)} i and the soft value δ({circumflex over (b)} i ) represents both a bit decision for the bit {circumflex over (b)} i and a confidence of the bit decision for the bit {circumflex over (b)} i .
16. The method of claim 12 wherein a modulation scheme of the received signal is a Gray-Mapped N Quadrature Amplitude Modulation, N-QAM, scheme having a modulation alphabet A containing 2 k =N symbols.
17. The method of claim 16 wherein processing the samples of the received signal to provide the soft values comprises, for each sample of the received signal, generating a soft value for each bit b i in b 0 . . . b k-1 of a corresponding received symbol utilizing less than N values of the modified maximum likelihood metric.
18. The method of claim 16 wherein processing the samples of the received signal to provide the soft values comprises, for each sample of the received signal:
computing values of the modified maximum likelihood metric defined as:
μ
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,
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,
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=
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5
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x
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+
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m
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1
+
1
5
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+
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3
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+
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+
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ln
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1
+
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)
wherein a received symbol s(b 0 , b 1 , b 2 , b 3 ) is a function of bits b 0 . . . b 3 , μ(s(*,*, b 2 , b 3 )) is the modified maximum likelihood metric for the received symbol s(b 0 , b 1 , b 2 , b 3 ) minimized over all possible choices of the bits b 0 and b 1 for given values for the bits b 2 and b 3 , and x is defined as:
x √{square root over (2/5)} ĥ H r ; and
generating soft values for each bit b i in b 0 . . . b 3 of a corresponding received symbol based on values μ(s(*,*,0,0)), μ(s(*,*,0,1)), μ(s(*,*,1,0)), and μ(s(*,*1,1)).
19. The method of claim 18 wherein generating the soft values for each bit b i in b 0 . . . b 3 of the corresponding received symbol comprises:
generating the soft value δ(b 0 ) for the bit b 0 in b 0 . . . b 3 of the corresponding received symbol according to:
δ
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b
0
)
=
sgn
(
Re
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^
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r
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[
μ
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s
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;
generating the soft value δ(b 1 ) for the bit b 1 in b 0 . . . b 3 of the corresponding received symbol according to:
δ
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=
sgn
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generating the soft value δ(b 2 ) for the bit b 2 in b 0 . . . b 3 of the corresponding received symbol according to:
δ( b 2 )=μ( s (*,*0,*))−μ( s (*,*,1,*)); and
generating the soft value δ(b 3 ) for the bit b 3 in b 0 . . . b 3 of the corresponding received symbol according to:
δ( b 3 )=μ( s (*,*,*,0))−μ( s (*,*,*,1));
wherein:
μ(s(*,*0,*)) is defined as:
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μ(s(*,*,1,*)) is defined as:
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and
μs(*,*,*,*)) is defined as:
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.
20. The method of claim 16 wherein processing the samples of the received signal to provide the soft values comprises, for each sample of the received signal:
computing values of the modified maximum likelihood metric for a corresponding received symbol s(b 0 , b 1 , b 2 , . . . , b k-1 ) minimized over all possible choices of bits b 0 and b 1 , where each value of the modified maximum likelihood metric corresponds to a different combination of values for bits b 2 through b k-1 ; and
generating soft values for each bit b i in b 0 , b 1 , b 2 , . . . , b k-1 of the corresponding received symbol s(b 0 , b 1 , b 2 , . . . , b k-1 ) based on the values of the modified maximum likelihood metric.