Modified Tomlinson-Harashima precoding method circuit for infinite impulse response (IIR) channels
View Patent ↗A precoding circuit for minimizing distortion of an input signal in a communication channel having a compound transfer function in the Z-Domain: H(z)=( 1 +a 1 .z −1 +a 2 .z −2 +a 3 .z 31 3 + . . . +a n .z −n )/( 1 +b 1 .z − +b 2 .z −2 +b −3 .z −3 + . . . +b p .z −p ). A feedback circuit comprises a first FIR filter and a transfer function corresponding to the inverse of a feedforward part of a transfer function of the communication channel. A feedforward circuit comprises a second FIR filter and a transfer function corresponding to the inverse of a feedback part of a transfer function of the communication channel. A first subtracting circuit subtracts a feedback signal of the feedback circuit from a feedforward signal of the feedforward circuit and outputs a difference signal which is added to a transmit end signal by a first adding circuit. The difference signal is also added to the input signal by a second adding circuit, the output from the second adding circuit is fed to a quantizing circuit which outputs a value kM which is subtracted from the input signal by a second subtracting circuit.
1. A precoding circuit for connecting to a communication channel ( 21 , 51 , 61 , 71 ) at a transmit end ( 22 ) thereof for minimising distortion of an input signal of range +M/2 to −M/2 being transmitted through the communication channel ( 21 , 51 , 61 , 71 ) between the transmit end ( 22 ) and a receive end ( 23 ) of the communication channel ( 21 , 51 , 61 , 71 ), whereby the distortion is due to a transfer function of the communication channel ( 21 , 51 , 61 , 71 ), the precoding circuit ( 20 , 50 , 60 , 70 ) comprising:
a feedback circuit ( 27 ) connected to the transmit end of the communication channel ( 21 , 51 , 61 , 71 ), and having a transfer function which is the inverse of a feedforward part of the transfer function of the communication channel,
a feedforward circuit ( 31 ) connected to the transmit end of the communication channel ( 21 , 51 , 61 , 71 ), and having a transfer function which is the inverse of a feedback part of the transfer function of the communication channel ( 21 , 51 , 61 , 71 ,),
a first circuit means ( 35 ) for subtracting a feedback signal of the feedback circuit ( 27 ) from a feedforward signal of the feedforward circuit ( 31 ), and for outputting a difference signal, which is the difference of the feedback and feedforward signals,
a second circuit means ( 39 ) for outputting a control signal of value kM derived from the difference signal and the input signal, where k is an integer which is a positive, negative or zero, and for selecting the value of k such that when the control signal is subtracted from the input signal at the transmit end ( 22 ) the value of the signal being outputted from the precoding circuit to the communication channel ( 21 , 51 , 61 , 71 ) is minimised, and
a third circuit means ( 40 ) for subtracting the control signal from the input signal upstream of the feedback and feedforward circuits ( 27 , 31 ).
2. A precoding circuit as claimed in claim 1 characterised in that the feedforward signal from the feedforward circuit ( 31 ) is applied to the transmit end of the communication channel ( 21 , 51 , 61 , 71 ) upstream of a node ( 30 ) from which the feedback circuit ( 27 ) derives its input from the transmit end of the communication channel ( 21 , 51 , 61 , 71 ).
3. A precoding circuit as claimed in claim 1 characterised in that the feedforward circuit ( 31 ) is upstream of the feedback circuit ( 27 ), or alternatively, the feedforward circuit ( 31 ) is downstream of the feedback circuit ( 27 ), and a node ( 34 ) from which the feedforward circuit derives its input from the transmit end ( 22 ) of the communication channel ( 21 , 51 , 61 , 71 ,), is downstream of the feedback circuit ( 27 ).
4. A precoding circuit as claimed in claim 1 characterised in that the first circuit means ( 35 ) comprises a first subtracting means ( 35 ) for subtracting the feedback signal from the feedforward signal and for outputting the difference signal, and preferably, a first adding means ( 37 ) is provided for adding the difference signal from the first circuit means ( 35 ) to the signal in the transmit end of the communication channel ( 21 , 51 , 61 , 71 ), and advantageously, the value of k of the control signal is selected by the second circuit means ( 39 ) such that when the control signal is subtracted from the input signal the value of the signal at the output from the precoding circuit ( 20 , 50 , 60 , 70 ), as it is fed to the communication channel ( 21 , 51 , 61 , 71 ), is within the range +M/2 to −M/2.
5. A precoding circuit as claimed in claim 1 characterised in that the difference signal and the input signal are added to provide an intermediate signal, and the intermediate signal is fed to the second circuit means ( 39 ), and the control signal is derived by the second circuit means ( 39 ) from the intermediate signal, and preferably, a second adding means ( 38 ) is provided for adding the input signal and the difference signal from the first circuit means ( 35 ) for providing the intermediate signal, and preferably, the second circuit means ( 39 ) comprises a quantising circuit ( 39 ) for deriving the control signal from the intermediate signal.
6. A precoding circuit as claimed in claim 1 characterised in that the third circuit means ( 40 ) comprises a second subtracting means ( 40 ) for subtracting the control signal from the input signal, and preferably, the difference signal from the first circuit means ( 35 ) is applied to the transmit end of the communication channel ( 21 , 51 , 61 , 71 ) intermediate respective nodes ( 30 , 34 ) from which the feedback circuit ( 27 ) and the feedforward circuit ( 31 ) derive their respective inputs from the transmit end of the communication channel ( 21 , 51 , 61 , 71 ).
7. A precoding circuit as claimed in claim 1 characterised in that the impulse response of the communication channel ( 21 , 51 , 61 , 71 ) is finite, and preferably, the feedforward part of the transfer function of the communication channel ( 21 , 51 , 61 , 71 ) can be broadly expressed in the Z-Domain by the equation:
H ( z )=(1 +a 1 .z −1 +a 2 .z −2 +a 3 .z −3 + . . . +a n .z −n )
where a is a filter coefficient multiplier, and z is a time of n time-steps.
8. A precoding circuit as claimed in claim 1 characterised in that the impulse response of the communication circuit ( 21 , 51 , 61 , 71 ) is infinite, and preferably, the feedback part of the transfer function of the communication channel ( 21 , 51 , 61 , 71 ) can be broadly expressed in the Z-Domain by the equation:
H
(
z
)
=
1
(
1
+
b
1
·
z
-
1
+
b
2
·
z
-
2
+
b
3
·
z
-
3
+
…
+
b
p
·
z
-
p
)
where b is a filter coefficient multiplier, and z is a time of p time-steps.
9. A precoding circuit as claimed in claim 1 characterised in that the compound transfer function of the communication channel ( 21 , 51 , 61 , 71 ) can be broadly expressed in the Z-Domain by the equation
H
(
z
)
=
(
1
+
a
1
·
z
-
1
+
a
2
·
z
-
2
+
a
3
·
z
-
3
+
…
+
a
n
·
z
-
n
)
(
1
+
b
1
·
z
-
1
+
b
2
·
z
-
2
+
b
3
·
z
-
3
+
…
+
b
p
·
z
-
p
)
where a and b are filter coefficient multipliers, and z is a time of n and p time-steps, and preferably, the transfer function of the feedback circuit ( 27 ) can be broadly expressed in the Z-Domain by the equation:
H
(
z
)
=
1
(
1
+
a
1
·
z
-
1
+
a
2
·
z
-
2
+
a
3
·
z
-
3
+
…
+
a
n
·
z
-
n
)
where a is a filter coefficient multiplier, and z is a time of n time-steps, and advantageously, the transfer function of the feedforward circuit ( 31 ) can be broadly expressed in the Z-Domain by the equation:
H ( z )=(1 +b 1 .z −1 +b 2 .z −2 +b 3 .z −3 + . . . +b p .z −p )
where b is a filter coefficient multiplier, and z is a time of p time-steps.
10. A precoding circuit as claimed in claim 1 characterised in that the precoding circuit is adapted for use with a subset of communication channels where the feedforward part of the transfer function is minimum phase.
11. A precoding circuit as claimed in claim 1 characterised in that a gain circuit means ( 52 ) is provided at the transmit end of the communication channel ( 21 , 51 , 61 , 71 ), downstream of the precoding circuit ( 20 , 50 , 60 , 70 ) for compensating for a first coefficient of the feedforward part of the transfer function of the communication channel ( 21 , 51 , 61 , 71 ), and preferably, the precoding circuit ( 20 , 50 , 60 , 70 ) is for equalising a subset of communication channels where the first coefficient of the feedforward part of the transfer function is equal to one, and advantageously, a third adding means ( 41 ) is provided at the receive end ( 23 ) of the communication channel ( 21 , 51 , 61 , 71 ) for adding a value kM to the signal at the receive end ( 23 ) of the communication channel ( 21 , 51 , 61 , 71 ) for facilitating recovery of the input signal at the receive end ( 23 ), the value of kM corresponding to the value of kM subtracted from the input signal at the transmit end ( 22 ) of the communication channel ( 21 , 51 , 61 , 71 ).
12. A precoding circuit as claimed in claim 1 characterised in that the precoding circuit is adapted for use with a non-linear constellation, and a first converting means ( 72 ) is provided for converting the signal at the transmit end of the communication channel ( 21 , 51 , 61 , 71 ), from being linear to being non-linear, and preferably, the first converting means ( 72 ) is located after the third circuit means, and preferably, a second converting means ( 73 ) is provided at the receive end of the communication channel ( 21 , 51 , 61 , 71 ) for converting the received signal at the receive end from non-linear to linear.
13. A communication circuit comprising the precoding circuit ( 20 , 50 , 60 , 70 ) as claimed in claim 1 .
14. A method for minimising distortion of a signal of range +M/2 to −M/2 being transmitted through a communication channel between a transmit end and a receive end of the communication channel, whereby the distortion is due to a transfer function of the communication channel, the method comprising the steps of:
feeding back the signal at the transmit end of the communication channel through a feedback circuit having a transfer function which is the inverse of a feedforward part of the transfer function of the communication channel,
feeding forward the signal at the transmit end of the communication channel through a feedforward circuit having a transfer function which is the inverse of a feedback part of the transfer function of the communication channel,
subtracting a feedback signal of the feedback circuit from a feedforward signal of the feedforward circuit to provide a difference signal,
deriving a control signal of value kM from the difference signal and an input signal, where k is an integer which is a positive, negative or zero, the value of k being selected such that when the control signal of value kM is subtracted from the input signal at the transmit end, the value of a signal being outputted from a precoding circuit to the communication channel is minimised, and
subtracting the control signal of value kM from the input signal upstream of the feedback and feedforward circuits.
15. A method as claimed in claim 14 characterised in that the feedforward signal from the feedforward circuit is applied to the transmit end of the communication channel upstream of a node from which the feedback circuit derives its input from the transmit end of the communication channel.
16. A method as claimed in claim 14 characterised in that the feedforward circuit is upstream of the feedback circuit.
17. A method as claimed in claim 14 characterised in that the feedback and feedforward signals are applied to the transmit end of the communication channel intermediate respective nodes from which the feedback circuit and the feedforward circuit derive their respective inputs at the transmit end of the communication channel, alternatively, the feedforward circuit is downstream of the feedback circuit, and a node from which the feedforward circuit derives input from the transmit end of the communication channel is downstream of the feedback circuit.
18. A method as claimed in claim 14 characterised in that the value of k of the control signal is selected such that when the control signal is subtracted from the input signal at the transmit end of the communication channel, the value of the signal being outputted from the precoding circuit to the communication channel at the transmit end thereof is within the range +M/2 to −M/2, and preferably, the difference signal and the input signal are added to provide an intermediate signal, and the control signal of value kM is derived from the intermediate signal.
19. A method as claimed in claim 14 characterised in that the impulse response of the communication channel is finite, and preferably, the feedforward part of the transfer function of the communication channel can be broadly expressed in the Z-Domain by the equation:
H ( z )=(1 +a 1 .z −1 +a 2 .z −2 +a 3 .z −3 + . . . +a n .z −n )
where a is a filter coefficient multiplier, and z is a time of n time-steps.
20. A method as claimed in claim 14 the impulse response of the communication channel is infinite, and preferably, the feedback part of the transfer function of the communication channel can be broadly expressed in the Z-Domain by the equation:
H
(
z
)
=
1
(
1
+
b
1
·
z
-
1
+
b
2
·
z
-
2
+
b
3
·
z
-
3
+
…
+
b
p
·
z
-
p
)
where b is a filter coefficient multiplier, and z is a time of a p time-steps, and preferably, the compound transfer function of the communication channel can be broadly expressed in the Z-Domain by the equation:
H
(
z
)
=
(
1
+
a
1
·
z
-
1
+
a
2
·
z
-
2
+
a
3
·
z
-
3
+
…
+
a
n
·
z
-
n
)
(
1
+
b
1
·
z
-
1
+
b
2
·
z
-
2
+
b
3
·
z
-
3
+
…
+
b
p
·
z
-
p
)
where a and b are filter coefficient multipliers, and z is a time of n and p time-steps, and advantageously, the transfer function of the feedback circuit can be broadly expressed in the Z-Domain by the equation:
H
(
z
)
=
1
(
1
+
a
1
·
z
-
1
+
a
2
·
z
-
2
+
a
3
·
z
-
3
+
…
+
a
n
·
z
-
n
)
where a is a filter coefficient multiplier, and z is a time of n time-steps, and preferably, the transfer function of the feedforward circuit can be broadly expressed in the Z-Domain by the equation:
H ( z )=(1 +b 1 .z −1 +b 2 .z −2 +b 3 .z −3 + . . . +b p .z −p )
where b is a filter coefficient multiplier, and z is a time of p time-steps.
21. A method as claimed in claim 14 characterised in that the method is adapted for use with a subset of communication channels where the feedforward part of the transfer function is minimum phase, and preferably, the signal being fed to the communication channel at the transmit end thereof is multiplied by a gain factor for compensating for a first coefficient of the feedforward part of the transfer function of the communication channel, and advantageously, the method is for equalising a subset of communication channels where the first coefficient of the feedforward part of the transfer function is equal to one, and preferably, the method further comprises the step of adding a value of kM to a signal at the receive end of the communication channel for recovering the input signal at the receive end, the value of kM corresponding to the value of kM subtracted from the input signal at the transmit end of the communication channel.