Time-domain equalizer and control method thereof
A time-domain equalizer for eliminating an echo signal from a received signal is provided. The received signal includes an original signal and the echo signal. The time-domain equalizer includes a time delay estimator, an amplitude amplifying ratio estimator and a phase shift estimator. The time delay estimator determines a delay amount maximizing a cost function to serve as an estimated delay amount of the echo signal relative to the original signal. The amplitude amplifying ratio estimator determines an estimated amplitude amplifying ratio of the echo signal relative to the original signal. The phase shift estimator determines an estimated phase shift of the echo signal relative to the original signal according to the estimated delay amount. The estimated delay amount, the estimated amplitude amplifying ratio and the estimated phase shift are used to set a filtering condition to be applied to the received signal.
1. A time-domain equalizer, for eliminating an echo signal from a received signal, the received signal comprising an original signal and the echo signal, the time-domain equalizer comprising:
a time delay estimator, determining a delay amount that maximizes a cost function to serve as an estimated delay amount of the echo signal relative to the original signal;
an amplitude amplifying ratio estimator, determining an estimated amplitude amplifying ratio of the echo signal, relative to the original signal, according to the estimated delay amount; and
a phase shift estimator, determining an estimated phase shift of the echo signal, relative to the original signal, according to the estimated delay amount;
wherein, the cost function is:
C (τ)=∥Σ k y [ k ] y* [ k+τ ]∥ 2 ,
where y[k] represents the received signal, k represents a sampling index, a signal y[k+τ] represents a delayed signal after the received signal is delayed by a time delay τ, and y*[k+τ] represents a conjugate of the delayed signal.
2. The time-domain equalizer according to claim 1 , wherein the amplitude amplifying ratio estimator determines the estimated amplitude amplifying ratio according to an equation:
α
^
_
=
C
(
τ
^
)
∑
k
∈
GI
y
[
k
]
y
*
[
k
+
μ
]
,
where kεGI represents that the amplitude amplifying ratio is calculated according to a sampling result corresponding to a guard interval of the original signal x, {circumflex over (τ)} represents the estimated delay amount generated by the time delay estimator, μ represents a length of fast Fourier transform (FFT) and y*[k+μ] represents a conjugate of another signal y delayed by FFT length μ.
3. The time-domain equalizer according to claim 1 , wherein the phase shift estimator determines a phase angle of a cost function calculation result C({circumflex over (τ)}) to serve as the estimated phase shift, and {circumflex over (τ)} represents the estimated delay amount generated by the time delay estimator.
4. The time-domain equalizer according to claim 1 , wherein the time delay estimator:
substitutes a plurality of candidate delay amounts into the cost function to generate a plurality of cost function calculation results, respectively; and
selects the candidate delay amount that generates a maximum cost function calculation result as the estimated delay amount according to the plurality of cost function calculation results.
5. The time-domain equalizer according to claim 1 , wherein a partial differentiation function is provided in advance, which is a result of partial differentiation of the cost function using the delay amount τ as a partial derivative; and the time delay estimator:
substitutes a plurality of candidate delay amounts into the partial differentiation function to generate a plurality of partial differentiation calculation results, respectively; and
selects the candidate delay amount that generates a partial differentiation calculation result that is closest to zero as the estimated delay amount according to the plurality of partial differential calculation results.
6. The time-domain equalizer according to claim 1 , wherein a partial differentiation function is provided in advance, which is a result of partial differentiation of the cost function using the delay amount τ as a partial derivative; the time delay estimator:
substitutes a plurality of candidate delay amounts into the cost function to generate a plurality of cost function calculation results, respectively;
selects the candidate delay amount capable of generating a maximum cost function calculation result as a preliminary estimated delay amount according to the plurality of cost function calculation results;
substitutes the preliminary estimated delay amount into the partial differentiation function to generate a first partial differentiation result;
selects a reference delay amount from the plurality of candidate delay amounts according to a sign of the first partial differentiation result;
substitutes the reference delay amount into the partial differentiation function to generate a second partial differentiation result; and
generates the estimated delay amount by performing interpolation according to the first partial differentiation result and the second partial differentiation result.
7. A control method for a time-domain equalizer, the time-equalizer for eliminating an echo signal from a received signal, the received signal comprising an original signal and the echo signal, the control method comprising:
a) determining a delay amount that maximizes a cost function to serve as an estimated delay amount of the echo signal relative to the original signal;
b) determining an estimated amplitude amplifying ratio and an estimated phase shift of the echo signal relative to the original signal according to the estimated delay amount; and
c) setting a filtering condition to be applied to the received signal according to the estimated delay amount, the estimated amplitude amplifying ratio and the estimated phase shift;
wherein, the cost function is:
C (τ)=∥Σ k y [ k ] y* [ k+τ ]∥ 2 ,
where y[k] represents the received signal, k represents a sampling index, a signal y[k+τ] represents a delayed signal after the received signal is delayed by a time delay τ, and y*[k+τ] represents a conjugate of the delayed signal.
8. The control method according to claim 7 , wherein step (b) determines the estimated amplitude amplifying ratio according to an equation:
α
^
_
=
C
(
τ
^
)
∑
k
∈
GI
y
[
k
]
y
*
[
k
+
μ
]
,
where kεGI represents that the amplitude amplifying ratio is calculated according to a sampling result corresponding to a guard interval of the original signal x, {circumflex over (τ)} represents the estimated delay amount generated in step (a), μ represents a length of fast Fourier transform (FFT) and y*[k+μ] represents a conjugate of another signal y delayed by FFT length μ.
9. The control method according to claim 7 , wherein step (b) comprises:
determining a phase angle of a cost function calculation result C({circumflex over (τ)}) to serve as the estimated phase shift, where {circumflex over (τ)} represents the estimated delay amount.
10. The control method according to claim 7 , wherein step (a) comprises:
substituting a plurality of candidate delay amounts into the cost function to generate a plurality of cost function calculation results, respectively; and
selecting the candidate delay amount that generates a maximum cost function calculation result to serve as the estimated delay amount according to the plurality of cost function calculation results.
11. The control method according to claim 7 , wherein a partial differentiation function is provided in advance, which is a result of partial differentiation of the cost function using the delay amount τ as a partial derivative; and step (a) comprises:
substituting a plurality of candidate delay amounts into the partial differentiation function to generate a plurality of partial differentiation calculation results, respectively; and
selecting the candidate delay amount that generates a partial differentiation calculation result that is closest to zero as the estimated delay amount according to the plurality of partial differential calculation results.
12. The control method according to claim 7 , wherein a partial differentiation function is provided in advance, which is a result of partial differentiation of the cost function using the delay amount τ as a partial derivative; and step (a) comprises:
substituting a plurality of candidate delay amounts into the cost function to generate a plurality of cost function calculation results, respectively;
selecting the candidate delay amount capable of generating a maximum cost function calculation result as a preliminary estimated delay amount according to the plurality of cost function calculation results;
substituting the preliminary estimated delay amounts into the partial differentiation function to generate a first partial differentiation result;
selecting a reference delay amount from the plurality of candidate delay amounts according to a sign of the first partial differentiation result;
substituting the reference delay amount into the partial differentiation function to generate a second partial differentiation result; and
generating the estimated delay amount by performing interpolation according to the first partial differentiation result and the second partial differentiation result.