Method of transmitting symbols
A method of transmitting symbols of a digital transmission constellation from a set thereof, ordered from a smallest to a greatest number of bits per symbol, may include identifying a first constellation from the set that is configured to communicate with a threshold error rate and has a greatest signal-to-noise ratio smaller than a signal-to-noise ratio of a received signal. The method may also include identifying a second constellation from the set that corresponds to a constellation with a number of bits per symbol immediately greater than the first constellation. The method may further include determining first and second probabilities of use of the first and second constellations that would generate an expected number of erroneous bits corresponding to the threshold error rate. The method may further include transmitting a symbol with a constellation selected randomly between the first and second constellations according to the first and second probabilities, respectively.
1. A method of transmitting symbols of a digital transmission constellation, the digital transmission constellation belonging to a set of digital transmission constellations ordered from a constellation with a smallest number of bits per symbol up to a constellation with a greatest number of bits per symbol, each digital transmission constellation having known respective error rate vs. signal-to-noise characteristics, the method comprising:
identifying a number of bits m of a first digital transmission constellation from the set of digital transmission constellations that is configured to communicate up to a threshold error rate β (T) and having a greatest signal-to-noise ratio smaller than a signal-to-noise ratio of a received signal γ;
identifying a number of bits {hacek over (m)} of a second digital transmission constellation from the set of digital transmission constellations that corresponds to a digital transmission constellation with a number of bits per symbol greater than the number of bits m of the first digital transmission constellation;
determining a first probability of use 1−P of the first digital transmission constellation and a second probability of use P of the second digital transmission constellation that would generate an expected number of received erroneous bits corresponding to the threshold error rate β (T) , the second probability of use being complementary to the first probability of use and being determined as a function of the error rate of the first and second digital transmission constellations P e (m) (γ) P e ({hacek over (m)}) (γ) corresponding to the signal-to-noise ratio of the received signal γ and the number of bits m of the first digital transmission constellation and the number of bits {hacek over (m)} of the second digital transmission constellation; and
transmitting a symbol with a digital transmission constellation selected randomly between the first and second digital constellations according to the first and second probabilities of use 1−P, P, respectively.
2. The method of claim 1 , wherein the error rate comprises one of a bit-error-rate and a block-error-rate.
3. The method of claim 1 , wherein the second probability of use P is determined according to the following equation:
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4. The method of claim 1 , wherein the second probability of use P is determined by at least:
determining a first discrete set of values (Ω) of the signal-to-noise ratio of the received signal;
determining a second discrete set of probability values ({ P 1 , P 2 , . . . , P L }) of the second probability of use;
filling in a look-up table of signal-to-noise ratio limit values for each combination of a value ( P i ) of the second discrete set with a digital transmission constellation of the set of digital transmission constellations by at least
for each signal-to-noise ratio of the received signal of the first discrete set (Ω)
determining an average number of bits of a symbol to be transmitted as an average of the number of bits {hacek over (m)} of a symbol of the second digital transmission constellation and the number of bits m of the first digital transmission constellation weighted with the second probability of use ( P i ) of the second discrete set and the complementary value thereof (1− P i ), respectively, and
estimating the error rate corresponding to an average number of bits of a symbol and of a value of the first discrete set, and
for the combination of a value ( P i ) of the second discrete set with the digital transmission constellation, storing a signal-to-noise ratio limit value configured to communicate at the threshold error rate β (T) ; and
determining the second probability of use P as a function of the signal-to-noise ratio of the received signal γ, by one of reading from the look-up table a probability value corresponding to the signal-to-noise ratio of the received signal γ and interpolating probability values corresponding to the signal-to-noise ratios limit values closest to the signal-to-noise ratio of the received signal γ.
5. The method of claim 1 , wherein the set of digital transmission constellations comprises at least one of BPSK, QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAM and 1024-QAM.
6. The method of claim 1 , wherein the symbols are transmitted according to a multi-carrier modulation; and wherein the steps of the method are executed for each used carrier.
7. A non-transitory computer-readable medium for use with circuit configured to transmit symbols of a digital transmission constellation, the digital transmission constellation belonging to a set of digital transmission constellations ordered from a constellation with a smallest number of bits per symbol up to a constellation with a greatest number of bits per symbol, each digital transmission constellation having known respective error rate vs. signal-to-noise characteristics, the computer-executable instructions for causing the circuit to perform the method comprising:
identifying a number of bits m of a first digital transmission constellation from the set of digital transmission constellations that is configured to communicate up to a threshold error rate β (T) and having a greatest signal-to-noise ratio smaller than a signal-to-noise ratio of a received signal γ;
identifying a number of bits {hacek over (m)} of a second digital transmission constellation from the set of digital transmission constellations that corresponds to a digital transmission constellation with a number of bits per symbol greater than the number of bits m of the first digital transmission constellation;
determining a first probability of use 1−P of the first digital transmission constellation and a second probability of use P of the second digital transmission constellation that would generate an expected number of received erroneous bits corresponding to the threshold error rate β (T) , the second probability of use being complementary to the first probability of use and being determined as a function of the error rate of the first and second digital transmission constellations P e (m) (γ) P e ({hacek over (m)}) (γ) corresponding to the signal-to-noise ratio of the received signal γ and the number of bits m of the first digital transmission constellation and the number of bits {hacek over (m)} of the second digital transmission constellation; and
transmitting a symbol with a digital transmission constellation selected randomly between the first and second digital constellations according to the first and second probabilities of use 1−P, P, respectively.
8. The non-transitory computer-readable medium of claim 7 , wherein the error rate comprises one of a bit-error-rate and a block-error-rate.
9. The non-transitory computer-readable medium of claim 7 , wherein the computer-executable instructions are for causing the circuit to determine the second probability of use P according to the following equation:
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10. The non-transitory computer-readable medium of claim 7 , wherein the computer-executable instructions for causing the circuit to determine the second probability of use P by at least:
determining a first discrete set of values (Ω) of the signal-to-noise ratio of the received signal;
determining a second discrete set of probability values ({ P 1 , P 2 , . . . , P L }) of the second probability of use;
filling in a look-up table of signal-to-noise ratio limit values for each combination of a value ( P i ) of the second discrete set with a digital transmission constellation of the set of digital transmission constellations by at least
for each signal-to-noise ratio of the received signal of the first discrete set (Ω)
determining an average number of bits of a symbol to be transmitted as an average of the number of bits {hacek over (m)} of a symbol of the second digital transmission constellation and the number of bits m of the first digital transmission constellation weighted with the second probability of use ( P i ) of the second discrete set and the complementary value thereof (1− P i ), respectively, and
estimating the error rate corresponding to an average number of bits of a symbol and of a value of the first discrete set, and
for the combination of a value ( P i ) of the second discrete set with the digital transmission constellation, storing a signal-to-noise ratio limit value configured to communicate at the threshold error β (T) ; and
determining the second probability of use P as a function of the signal-to-noise ratio of the received signal γ, by one of reading from the look-up table a probability value corresponding to the signal-to-noise ratio of the received signal γ and interpolating probability values corresponding to the signal-to-noise ratios limit values closest to the signal-to-noise ratio of the received signal γ.
11. The non-transitory computer-readable medium of claim 7 , wherein the set of digital transmission constellations comprises at least one of BPSK, QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAM and 1024-QAM.
12. The non-transitory computer-readable medium of claim 7 , wherein the symbols are transmitted according to a multi-carrier modulation; and wherein the computer-executable instructions are for causing the circuit to execute for each used carrier.
13. A communication system comprising:
a circuit configured to transmit symbols of a digital transmission constellation, the digital transmission constellation belonging to a set of digital transmission constellations ordered from a constellation with a smallest number of bits per symbol up to a constellation with a greatest number of bits per symbol, each digital transmission constellation having known respective error rate vs. signal-to-noise characteristics, wherein said circuit is configured to transmit the symbols of the digital constellation by at least
identifying a number of bits m of a first digital transmission constellation from the set of digital transmission constellations that is configured to communicate up to a threshold error rate β (T) and having a greatest signal-to-noise ratio smaller than a signal-to-noise ratio of a received signal γ,
identifying a number of bits {hacek over (m)} of a second digital transmission constellation from the set of digital transmission constellations that corresponds to a digital transmission constellation with a number of bits per symbol greater than that of the first digital transmission constellation,
determining a first probability of use 1−P of the first digital transmission constellation and a second probability of use P of the second digital transmission constellation that would generate an expected number of received erroneous bits corresponding to the threshold error rate β (T) , the second probability of use being complementary to the first probability of use and being determined as a function of the error rate of the first and second digital transmission constellations P e (m) (γ) P e ({hacek over (m)}) (γ) corresponding to the signal-to-noise ratio of the received signal γ and a number of bits m of the first digital transmission constellation and the number of bits {hacek over (m)} of the second digital transmission constellation, and
transmitting a symbol with a digital transmission constellation selected randomly between the first and second digital constellations according to the first and second probabilities of use 1−P, P, respectively.
14. The communication system of claim 13 , wherein the error rate comprises one of a bit-error-rate and a block-error-rate.
15. The communication system of claim 13 , wherein said circuit is configured to determine the second probability of use P according to the following equation:
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m
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β
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16. The communication system of claim 13 , wherein said circuit is configured to determine the second probability of use P by at least:
determining a first discrete set of values (Ω) of the signal-to-noise ratio of the received signal;
determining a second discrete set of probability values ({ P 1 , P 2 , . . . , P L }) of the second probability of use;
filling in a look-up table of signal-to-noise ratio limit values for each combination of a value ( P i ) of the second discrete set with a digital transmission constellation of the set of digital transmission constellations by at least
for each signal-to-noise ratio of the received signal of the first discrete set (Ω)
determining an average number of bits of a symbol to be transmitted as an average of the number of bits {hacek over (m)} of a symbol of the second digital transmission constellation and the number of bits m of the first digital transmission constellation weighted with the second probability of use ( P i ) of the second discrete set and the complementary value thereof (1− P i ), respectively, and
estimating the error rate corresponding to an average number of bits of a symbol and of a value of the first discrete set, and
for the combination of a value ( P i ) of the second discrete set with the digital transmission constellation, storing a signal-to-noise ratio limit value configured to communicate at the threshold error rate β (T) ; and
determining the second probability of use P as a function of the signal-to-noise ratio of the received signal γ, by one of reading from the look-up table a probability value corresponding to the signal-to-noise ratio of the received signal γ and interpolating probability values corresponding to the signal-to-noise ratios limit values closest to the signal-to-noise ratio of the received signal γ.
17. The communication system of claim 13 , wherein the set of digital transmission constellations comprises at least one of BPSK, QPSK, 8-QAM, 16-QAM, 64-QAM, 256-QAM and 1024-QAM.
18. The communication system of claim 13 , wherein said circuit is configured to transmit symbols according to a multi-carrier modulation and execute for each used carrier.
19. The communication system of claim 13 , wherein said circuit comprises a powerline transmission circuit.