Systems and methods for blind echo cancellation
System and method for blind echo cancellation in a received terahertz signal in a pulsed terahertz system for imaging or spectroscopy. Blind signal processing methods estimate the impulse response of the reflection mechanism and do not require a reference measurement to be taken. The reference signal may be recovered using a successive approach wherein the reference is first estimated using cross-correlation with the received signal and the received signal is represented as a function of the reference signal. For each successive echo, the calculated echo may be subtracted from the received signal and then the estimate of the reference signal is refined. Using an analytical approach, the parameters of a transfer function modeling the reflection mechanism may be estimated by optimizing a cost function.
1. A method for canceling echoes in a terahertz signal, the method comprising the steps of:
receiving a terahertz signal containing echoes;
estimating a reference signal from the received signal;
calculating the echoes as a function of the reference signal;
for at least one of the successive echoes,
subtracting the calculated echo from the received signal to form a refined reference signal; and
re-calculating the echoes as a function of the refined reference signal.
2. The method of claim 1 wherein the steps of calculating the echoes and re-calculating the echoes comprises:
estimating the time-shift and amplitude of each echo as a function of the corresponding reference signal.
3. The method of claim 2 wherein the steps of subtracting the calculated echo and re-calculating the echoes is repeated until a threshold is reached.
4. The method of claim 3 wherein the threshold is defined by the refined reference signal being recovered over a defined portion of echo period.
5. The method of claim 3 wherein the threshold is defined by the number of iterations performed.
6. The method of claim 3 wherein the threshold is defined by difference between refined reference signal and the prior calculation of the refined reference signal.
7. The method of claim 2 wherein the step of estimating the reference signal uses cross-correlation of the received signal.
8. The method of claim 2 wherein the received signal is expressed as a sum of scaled, time-shifted reference signals.
9. A method for canceling echoes in a terahertz signal, the method comprising the steps of:
receiving a terahertz signal containing echoes;
calculating a reference signal as a function of the received signal; and
estimating system parameters of a reflection mechanism by minimizing the energy of the calculated reference signal; and
deconvolving the received signal with an inverse transfer function using the system parameters to remove at least one of the echoes.
10. The method of claim 9 wherein the function of the reference signal is modeled as a function of the received signal:
{circumflex over (x)} ref ( t )= X in −βX in ( t− 2 d )
where β is a system parameter representing the gain and d is a system parameter representing the time-shift.
11. The method of claim 9 wherein the inverse transfer function is based on a transfer function model of a single slab medium in a vacuum.
12. The method of claim 11 wherein the transfer function is:
h
S
(
Z
)
=
α
Z
-
d
1
-
β
Z
-
2
d
where
α
=
4
n
(
n
+
1
)
2
,
β
=
(
n
-
1
n
+
1
)
2
,
and
d
=
nL
C
f
samp
where n is the refractive index, L is the thickness of the slab and f samp is the sampling frequency.
13. A system for canceling echoes in a terahertz signal, the system comprising:
a terahertz signal receiver for receiving a terahertz signal containing echoes;
an estimator for estimating a reference signal from the received signal;
an echo subtracter for subtracting an echo from the received signal to form a refined reference signal; and
a signal calculator for calculating the echoes as a function of the reference signal, and for calculating the echoes as a function of the refined reference signal.
14. The system of claim 13 wherein the signal calculator estimates the time-shift and amplitude of each echo as a function of corresponding reference signal.
15. The system of claim 14 wherein the echo subtracter and signal calculator repeatedly subtract an echo and calculate the echoes as a function of the refined reference signal until a threshold is reached.
16. The system of claim 14 wherein the estimator uses cross-correlation of the received terahertz signal.
17. The system of claim 14 wherein the signal calculator expresses the received signal as a sum of scaled, time-shifted reference signals.