US4709374A
Expired / Lapsed
US
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Technique for decision-directed equalizer train/retrain
Assignee: AT&T Inc
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Filing: 1984-07-05
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Granted: 1987-11-24
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Expires: 2004-07-05
Abstract
Abstract An adaptive equalizer for data signals is allowed to start up and train in a wholly decision-directed mode but is precluded from converging to an incorrect state by inhibiting equalizer updating for equalizer output values which fall within a predetermined null zone.
Inventors
- 👤 Cecil W. Farrow
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-08 06:39
CPC Classifications
H; H04; H04L; H04L27/00; H04L27/01
Claims Analysis
Total Claims: 46
Claim 1
Independent Claim
281 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted points of a predetermined signal constellation, said apparatus comprising equalizing means having a plurality of states and operative in each of said states for generating in response to said received data signal an equalizer output point associated with each transmitted point, in at least one of said states at least one of said equalizer output points being more distant in said constellation from the associated transmitted point than it is from at least one other point of said constellation and at least another of said equalizer output points being closer in said constellation to the associated transmitted point than it is to any other point of said constellation, means operative in response to each equalizer output point for forming as a decision as to the value of the associated transmitted signal point the point of said constellation to which said each equalizer output point is closest, there being associated with the value of said each equalizer output point and its associated decision a decision-directed error value, means normally operative for updating said equalizing means from its current one of said states to a new one of said states for each of said equalizer output points, said updating being such that the mean-squared value of the decision-directed errors associated with the equalizer output points generated by said equalizing means is minimized, and means for inhibiting the operation of said updating means for at least said one of said equalizer output points while not inhibiting the operation of said updating means for said another of said equalizer output points.
Claim 2
Dependent Claim
281 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted points of a predetermined signal constellation, said apparatus comprising equalizing means having a plurality of states and operative in each of said states for generating in response to said received data signal an equalizer output point associated with each transmitted point, in at least one of said states at least one of said equalizer output points being more distant in said constellation from the associated transmitted point than it is from at least one other point of said constellation and at least another of said equalizer output points being closer in said constellation to the associated transmitted point than it is to any other point of said constellation, means operative in response to each equalizer output point for forming as a decision as to the value of the associated transmitted signal point the point of said constellation to which said each equalizer output point is closest, there being associated with the value of said each equalizer output point and its associated decision a decision-directed error value, means normally operative for updating said equalizing means from its current one of said states to a new one of said states for each of said equalizer output points, said updating being such that the mean-squared value of the decision-directed errors associated with the equalizer output points generated by said equalizing means is minimized, and means for inhibiting the operation of said updating means for at least said one of said equalizer output points while not inhibiting the operation of said updating means for said another of said equalizer output points.
Claim 3
Dependent Claim
20 words
The invention of claim 1 wherein said updating means updates said equalizing means utilizing a mean-squared error stochastic updating algorithm.
Claim 4
Dependent Claim
30 words
The invention of claim 1 wherein said decision-directed error value is a function of the difference between the value of said each equalizer output point and its said associated decision.
Claim 5
Dependent Claim
47 words
The invention of claim 1 wherein each coordinate of at least one of the points of said constellation has one of the values ±1 and ±3 and wherein the magnitude of said one of said equalizer output points is greater than √2 and less than 2 √2.
Claim 6
Dependent Claim
61 words
The invention of claim 1 wherein each coordinate of at least one of the points of said constellation has one of the values of ±1 and ±3 and wherein the magnitude of one of the coordinates of said one of said equalizer output points is between unity and 2 and the magnitude of the other coordinate thereof is less than 2.
Claim 7
Dependent Claim
281 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted data symbols, said apparatus comprising means for equalizing said received signal to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, means for forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, there being associated with said each equalizer output a decision-directed error whose value is a function of at least the value of said each equalizer output and the associated decision, and an actual error whose value is a function of at least said each equalizer output value and the value of the respective transmitted symbol, said decision-directed error and said actual error being different from one another when said each equalizer output has at least a first particular equalizer output value while the respective transmitted symbol has at least a first particular data symbol value and said decision-directed error and said actual error being the same when each equalizer output has at least a second particular equalizer output value while the respective transmitted symbol has at least a second particular data symbol value, means normally operative for updating the transfer characteristic of said equalizing means for said each equalizer output as a function at least of the value of the associated decision-directed error, and means for inhibiting the operation of said updating means at least when said each equalizer output has said first particular equalizer output value while not inhibiting the operation of said updating means when said each equalizer output has said second particular equalizer output value.
Claim 8
Dependent Claim
281 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted data symbols, said apparatus comprising means for equalizing said received signal to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, means for forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, there being associated with said each equalizer output a decision-directed error whose value is a function of at least the value of said each equalizer output and the associated decision, and an actual error whose value is a function of at least said each equalizer output value and the value of the respective transmitted symbol, said decision-directed error and said actual error being different from one another when said each equalizer output has at least a first particular equalizer output value while the respective transmitted symbol has at least a first particular data symbol value and said decision-directed error and said actual error being the same when each equalizer output has at least a second particular equalizer output value while the respective transmitted symbol has at least a second particular data symbol value, means normally operative for updating the transfer characteristic of said equalizing means for said each equalizer output as a function at least of the value of the associated decision-directed error, and means for inhibiting the operation of said updating means at least when said each equalizer output has said first particular equalizer output value while not inhibiting the operation of said updating means when said each equalizer output has said second particular equalizer output value.
Claim 9
Dependent Claim
20 words
The invention of claim 6 wherein said updating means updates said equalizing means utilizing a mean-squared error stochastic updating algorithm.
Claim 10
Dependent Claim
32 words
The invention of claim 6 wherein said updating means updates said equalizing means in such a way that the mean-squared value of the decision-directed errors associated with said equalizer output is minimized.
Claim 11
Dependent Claim
325 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted signal points selected from a predetermined constellation, said apparatus comprising equalizing means having a plurality of operating states, each said state having an associated output constellation and an associated error function value, said associated error function value being a measure of the distance between the points of the output constellation associated with said each state and the respective closest points of said predetermined constellation, said function having at least first minimum corresponding to a first one of said states whose associated output constellation is substantially identical to said predetermined constellation and at least a second minimum corresponding to a second one of said states whose associated output constellation is substantially different from said predetermined constellation, said equalizing means being operative in response to said received signal for generating for each different transmitted signal point an equalizer output representing a respective point of the output constellation associated with the current one of said states, means for forming for each said equalizer output an associated decision as to the value of the respective transmitted signal point, means operative for repetitively updating said equalizing means to establish it in a state whose associated error function value is substantially at a minimum point of said function, said updating means including means normally operative for updating said equalizing means to a new state for each said equalizer output, and means for inhibiting the operation of said updating means when the value of said each equalizer output is in a predetermined range of values that includes predetermined ones of the signal points of said output constellation associated with said second state but does not include any of the signal points of said predetermined constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is outside of said predetermined range.
Claim 12
Dependent Claim
325 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted signal points selected from a predetermined constellation, said apparatus comprising equalizing means having a plurality of operating states, each said state having an associated output constellation and an associated error function value, said associated error function value being a measure of the distance between the points of the output constellation associated with said each state and the respective closest points of said predetermined constellation, said function having at least first minimum corresponding to a first one of said states whose associated output constellation is substantially identical to said predetermined constellation and at least a second minimum corresponding to a second one of said states whose associated output constellation is substantially different from said predetermined constellation, said equalizing means being operative in response to said received signal for generating for each different transmitted signal point an equalizer output representing a respective point of the output constellation associated with the current one of said states, means for forming for each said equalizer output an associated decision as to the value of the respective transmitted signal point, means operative for repetitively updating said equalizing means to establish it in a state whose associated error function value is substantially at a minimum point of said function, said updating means including means normally operative for updating said equalizing means to a new state for each said equalizer output, and means for inhibiting the operation of said updating means when the value of said each equalizer output is in a predetermined range of values that includes predetermined ones of the signal points of said output constellation associated with said second state but does not include any of the signal points of said predetermined constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is outside of said predetermined range.
Claim 13
Dependent Claim
34 words
The invention of claim 9 wherein said error function value is the mean squared value of the distance between each point of said associated output constellation and the nearest point of said predetermined constellation.
Claim 14
Dependent Claim
70 words
The invention of claim 10 wherein each coordinate of at least one of the points of said predetermined constellation has one of the values ±1 and ±3, each coordinate of at least one of the points of said output constellation associated with said second one of said states has one of the values ±0.4 and ±1.2, and said range of values includes the values whose coordinates are substantially (±1.2, ±1.2).
Claim 15
Dependent Claim
24 words
The invention of claim 11 wherein said range of values includes values whose magnitudes are greater than about 1.70 and less than about 2.83.
Claim 16
Dependent Claim
75 words
The invention of claim 10 wherein each coordinate of at least one of the points of said predetermined constellation has one of the values ±1 and ±3, each coordinate of at least one of the points of said output constellation associated with said second one of said states has one of the values ±0.4 and ±1.2, and said range of values includes the values whose coordinates are substantially (±0.4, ±1.2), (±1.2, ±0.4) and (±1.2, ±1.2).
Claim 17
Dependent Claim
38 words
The invention of claim 13 wherein each of at least one of the values in said range has a first coordinate whose magnitude is between 1.2 and 2 and a second coordinate whose magnitude is less than 2.
Claim 18
Dependent Claim
205 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted data symbols of a predetermined signal constellation, said apparatus comprising means for equalizing said received signal to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, means for forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, means normally operative for updating the transfer characteristic of said equalizing means for said each equalizer output as a function at least of the value of said each equalizer output and its associated decision, and means for inhibiting the operation of said updating means when the value of said each equalizer output is one of a predetermined plurality of values each of whose magnitudes is greater than the magnitude of each of a first plurality of the data symbols of said constellation and less than the magnitude of each of a second plurality of the data symbols of said constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is other than one of said predetermined plurality of values.
Claim 19
Dependent Claim
205 words
Apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted data symbols of a predetermined signal constellation, said apparatus comprising means for equalizing said received signal to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, means for forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, means normally operative for updating the transfer characteristic of said equalizing means for said each equalizer output as a function at least of the value of said each equalizer output and its associated decision, and means for inhibiting the operation of said updating means when the value of said each equalizer output is one of a predetermined plurality of values each of whose magnitudes is greater than the magnitude of each of a first plurality of the data symbols of said constellation and less than the magnitude of each of a second plurality of the data symbols of said constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is other than one of said predetermined plurality of values.
Claim 20
Dependent Claim
20 words
The invention of claim 15 wherein said updating means updates said equalizing means utilizing a mean-squared error stochastic updating algorithm.
Claim 21
Dependent Claim
34 words
The invention of claim 15 wherein said updating means updates said equalizing means in such a way that the mean-squared value of the difference between each equalizer output and its associated decision is minimized.
Claim 22
Dependent Claim
46 words
The invention of claim 15 wherein each coordinate of at least one of the data symbols of said predetermined constellation has one of the values ±1 and ±3 and wherein said magnitudes of said predetermined plurality of values are greater than √2 and less than 2√2.
Claim 23
Dependent Claim
78 words
The invention of claim 15 wherein each of the data symbols of said predetermined constellation has a pair of coordinates, wherein each coordinate of at least one of the data symbols of said predetermined constellation has one of the values of ±1 and ±3 and wherein the magnitude of one of the coordinates of each of said predetermined plurality of values is between unity and 2 and the magnitude of the other coordinate thereof is less than 2.
Claim 24
Independent Claim
292 words
A method for use in conjunction with apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted points of a predetermined signal constellation, said apparatus comprising equalizing means having a plurality of states and operative in each of said states for generating in response to said received data signal an equalizer output point associated with each transmitted point, in at least one of said states at least one of said equalizer output points being more distant in said constellation from the associated transmitted point than it is from at least one other point of said constellation and at least another of said equalizer output points being closer in said constellation to the associated transmitted point than it is to any other point of said constellation; means operative in response to each equalizer output point for forming as a decision as to the value of the associated transmitted signal point the point of said constellation to which said each equalizer output point is closest, there being associated with the value of said each equalizer output point and its associated decision a decision-directed error value; and means normally operative for updating said equalizing means from its current one of said states to a new one of said states for each of said equalizer output points, said updating being such that the mean-squared value of the decision-directed errors associated with the equalizer output points generated by said equalizing means is minimized; said method comprising the step of inhibiting the operation of said updating means for at least said one of said equalizer output points while not inhibiting the operation of said updating means for said another of said equalizer output points.
Claim 25
Independent Claim
292 words
A method for use in conjunction with apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted points of a predetermined signal constellation, said apparatus comprising equalizing means having a plurality of states and operative in each of said states for generating in response to said received data signal an equalizer output point associated with each transmitted point, in at least one of said states at least one of said equalizer output points being more distant in said constellation from the associated transmitted point than it is from at least one other point of said constellation and at least another of said equalizer output points being closer in said constellation to the associated transmitted point than it is to any other point of said constellation; means operative in response to each equalizer output point for forming as a decision as to the value of the associated transmitted signal point the point of said constellation to which said each equalizer output point is closest, there being associated with the value of said each equalizer output point and its associated decision a decision-directed error value; and means normally operative for updating said equalizing means from its current one of said states to a new one of said states for each of said equalizer output points, said updating being such that the mean-squared value of the decision-directed errors associated with the equalizer output points generated by said equalizing means is minimized; said method comprising the step of inhibiting the operation of said updating means for at least said one of said equalizer output points while not inhibiting the operation of said updating means for said another of said equalizer output points.
Claim 26
Dependent Claim
18 words
The method of claim 20 wherein said updating step is performed utilizing a mean-squared error stochastic updating algorithm.
Claim 27
Dependent Claim
30 words
The method of claim 20 wherein said decision-directed error value is a function of the difference between the value of said each equalizer output point and its said associated decision.
Claim 28
Dependent Claim
46 words
The method of claim 20 wherein each coordinate of at least one of the points of said constellation has one of the values ±1 and ±3 and wherein the magnitude of said one of said equalizer output points is greater than √2 and less than 2√2.
Claim 29
Dependent Claim
61 words
The method of claim 20 wherein each coordinate of at least one of the points of said constellation has one of the values of ±1 and ±3 and wherein the magnitude of one of the coordinates of said one of said equalizer output points is between unity and 2, and the magnitude of the other coordinate thereof is less than 2.
Claim 30
Independent Claim
271 words
A method for processing a received data signal transmitted over a communication channel, said received data signal representing a succession of transmitted data symbols, said method comprising the steps of equalizing said received signal in accordance with a selected transfer characteristics to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, there being associated with said each equalizer output a decision-directed error whose value is a function of at least the value of said each equalizer output and the associated decision, and an actual error whose value is a function of at least said equalizer output value and the value of the respective transmitted symbol, said decision-directed error and said actual error being different from one another when said each equalizer output has at least a first particular equalizer output value while the respective transmitted symbol has at least a first particular data symbol value and said decision-directed error and said actual error being the same when each equalizer output has at least a second particular equalizer output value while the respective transmitted symbol has at least a second particular data symbol value, normally updating said transfer characteristic for said each equalizer output as a function at least of the value of the associated decision-directed error, and inhibiting said updating at least when said each equalizer output has said first particular equalizer output value while not inhibiting the operation of said updating means when said each equalizer output has said second particular equalizer output values.
Claim 31
Independent Claim
271 words
A method for processing a received data signal transmitted over a communication channel, said received data signal representing a succession of transmitted data symbols, said method comprising the steps of equalizing said received signal in accordance with a selected transfer characteristics to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, there being associated with said each equalizer output a decision-directed error whose value is a function of at least the value of said each equalizer output and the associated decision, and an actual error whose value is a function of at least said equalizer output value and the value of the respective transmitted symbol, said decision-directed error and said actual error being different from one another when said each equalizer output has at least a first particular equalizer output value while the respective transmitted symbol has at least a first particular data symbol value and said decision-directed error and said actual error being the same when each equalizer output has at least a second particular equalizer output value while the respective transmitted symbol has at least a second particular data symbol value, normally updating said transfer characteristic for said each equalizer output as a function at least of the value of the associated decision-directed error, and inhibiting said updating at least when said each equalizer output has said first particular equalizer output value while not inhibiting the operation of said updating means when said each equalizer output has said second particular equalizer output values.
Claim 32
Dependent Claim
17 words
The method of claim 25 wherein said updating is performed utilizing a mean-squared error stochastic updating algorithm.
Claim 33
Dependent Claim
29 words
The method of claim 25 wherein said updating is performed in such a way that the mean-squared value of the decision-directed errors associated with said equalizer output is minimized.
Claim 34
Independent Claim
336 words
A method for use in conjunction with apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted signal points selected from a predetermined constellation, said apparatus comprising equalizing means having a plurality of operating states, each said state having an associated output constellation and an associated error function value, said associated error function value being a measure of the distance between the points of the output constellation associated with said each state and the respective closest points of said predetermined constellation, said function having at least first minimum corresponding to a first one of said states whose associated output constellation is substantially identical to said predetermined constellation and at least a second minimum corresponding to a second one of said states whose associated output constellation is substantially different from said predetermined constellation, said equalizing means being operative in response to said received signal for generating for each different transmitted signal point an equalizer output representing a respective point of the output constellation associated with the current one of said states; means for forming for each said equalizer output an associated decision as to the value of the respective transmitted signal point; and means operative for repetitively updating said equalizing means to establish it in a state whose associated error function value is substantially at a minimum point of said function, said updating means including means normally operative for updating said equalizing means to a new state for each said equalizer output, said method comprising the step of inhibiting the operation of said updating means when the value of said each equalizer output is in a predetermined range of values that includes predetermined ones of the signal points of said output constellation associated with said second state but does not include any of the signal points of said predetermined constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is outside of said predetermined range.
Claim 35
Independent Claim
336 words
A method for use in conjunction with apparatus for processing a received data signal transmitted to said apparatus over a communication channel, said received data signal representing a succession of transmitted signal points selected from a predetermined constellation, said apparatus comprising equalizing means having a plurality of operating states, each said state having an associated output constellation and an associated error function value, said associated error function value being a measure of the distance between the points of the output constellation associated with said each state and the respective closest points of said predetermined constellation, said function having at least first minimum corresponding to a first one of said states whose associated output constellation is substantially identical to said predetermined constellation and at least a second minimum corresponding to a second one of said states whose associated output constellation is substantially different from said predetermined constellation, said equalizing means being operative in response to said received signal for generating for each different transmitted signal point an equalizer output representing a respective point of the output constellation associated with the current one of said states; means for forming for each said equalizer output an associated decision as to the value of the respective transmitted signal point; and means operative for repetitively updating said equalizing means to establish it in a state whose associated error function value is substantially at a minimum point of said function, said updating means including means normally operative for updating said equalizing means to a new state for each said equalizer output, said method comprising the step of inhibiting the operation of said updating means when the value of said each equalizer output is in a predetermined range of values that includes predetermined ones of the signal points of said output constellation associated with said second state but does not include any of the signal points of said predetermined constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is outside of said predetermined range.
Claim 36
Dependent Claim
33 words
The method of claim 28 wherein said error function value is the mean-squared value of the distance between each point of said associated output constellation and the nearest point of said predetermined constellation.
Claim 37
Dependent Claim
70 words
The method of claim 29 wherein each coordinate of at least one of the points of said predetermined constellation has one of the values ±1 and ±3, each coordinate of at least one of the points of said output constellation associated with said second one of said states has one of the values ±0.4 and ±1.2, and said range of values includes the values whose coordinates are substantially (±1.2, ±1.2).
Claim 38
Dependent Claim
24 words
The method of claim 30 wherein said range of values includes values whose magnitudes are greater than about 1.70 and less than about 2.83.
Claim 39
Dependent Claim
76 words
The method of claim 29 wherein each coordinate of at least one of the points of said predetermined constellation has one of the values ±1 and 35 3, each coordinate of at least one of the points of said output constellation associated with said second one of said states has one of the values ±0.4 and ±1.2, and said range of values includes the values whose coordinates are substantially (±0.4, ±1.2), (±1.2, ±0.4) and (±1.2, ±1.2).
Claim 40
Dependent Claim
38 words
The method of claim 32 wherein each of at least one of the values in said range has a first coordinate whose magnitude is between 1.2 and 2 and a second coordinate whose magnitude is less than 2.
Claim 41
Independent Claim
197 words
A method for processing a received data signal transmitted over a communication channel, said received data signal representing a succession of transmitted data symbols of a predetermined signal constellation, said method comprising the steps of equalizing said received signal in accordance with a selected transfer characteristic to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, normally updating said transfer characteristic for said each equalizer output as a function at least of the value of said each equalizer output and its associated decision, and inhibiting said updating step when the value of said each equalizer output is one of a predetermined plurality of values each of whose magnitudes is greater than the magnitude of each of a first plurality of the data symbols of said constellation and less than the magnitude of each of a second plurality of the data symbols of said constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is other than one of said predetermined plurality of values.
Claim 42
Independent Claim
197 words
A method for processing a received data signal transmitted over a communication channel, said received data signal representing a succession of transmitted data symbols of a predetermined signal constellation, said method comprising the steps of equalizing said received signal in accordance with a selected transfer characteristic to form a succession of equalizer outputs, each equalizer output representing a respective one of the transmitted symbols, forming for said each equalizer output an associated decision as to the value of the respective transmitted symbol, normally updating said transfer characteristic for said each equalizer output as a function at least of the value of said each equalizer output and its associated decision, and inhibiting said updating step when the value of said each equalizer output is one of a predetermined plurality of values each of whose magnitudes is greater than the magnitude of each of a first plurality of the data symbols of said constellation and less than the magnitude of each of a second plurality of the data symbols of said constellation, while not inhibiting the operation of said updating means when the value of said each equalizer output is other than one of said predetermined plurality of values.
Claim 43
Dependent Claim
22 words
The method of claim 34 wherein in said updating step said transfer characteristic is updated utilizing a mean-squared error stochastic updating algorithm.
Claim 44
Dependent Claim
36 words
The method of claim 34 wherein in said updating step said transfer characteristic is updated in such a way that the mean-squared value of the difference between each equalizer output and its associated decision is minimized.
Claim 45
Dependent Claim
46 words
The method of claim 34 wherein each coordinate of at least one of the data symbols of said predetermined constellation has one of the values ±1 and ±3 and wherein said magnitudes of said predetermined plurality of values are greater than √2 and less than 2√2.
Claim 46
Dependent Claim
78 words
The method of claim 34 wherein each of the data symbols of said predetermined constellation has a pair of coordinates, wherein each coordinate of at least one of the data symbols of said predetermined constellation has one of the values of ±1 and ±3 and wherein the magnitude of one of the coordinates of each of said predetermined plurality of values is between unity and 2 and the magnitude of the other coordinate thereof is less than 2.
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