Digital Signal Processing Reference
In-Depth Information
forcing qpsk samples from the output time-domain signal vector in a qpsk
constellation shape. This, in combination with a closed-loop system which
continuously tries to minimize the distance between the unaffected portions
of the spectral footprint of the in- and output, allows issr to recover the orig-
inal signal. The underlying structure makes that the issr algorithm should be
classified as a guided optimization technique, closely related to evolutionary
algorithms. This finding is quite exciting because it puts things in a different
light. The experimental results are delayed until after the presentation of the
next section, which covers some of the practical implementation aspects of
issr on a digital processing system.
3.3
Implementation aspects of the ISSR algorithm
The fast-varying location of deep fades in an environment with a low coherence
time requires a certain level of flexibility, which is only available in a digital
system. However, the feedback system introduced by Figure 3.3 is conceived
as an analog, continuous-time system. In order to implement the issr decoder
as a digital algorithm, the feedback loop must be translated from a continuous-
time to a discrete-time representation. For this purpose, the continuous-time
integration element
G/s
from Figure 3.3 must be converted from the s- to the
z-domain. This is done using the
Forward Euler
(fe) transformation [Opp03]
which results in the discrete-time integrator shown in Figure 3.5. The two delay
elements
D
1
and
D
2
allow to cut the loop in two halves, which enables to
implement the entire issr system in the form of an iterative algorithm.
Only two parameters in Figure 3.5 are still to be identified. The first gain el-
ement,
B
=
GT
s
, is determined both by the gain
G
of the continuous-time
+
G/s
discrete-time integrator
controls stability
+
D
1
B
A
+
controls step size
A.B
z-A
H(z) =
D
2
Figure 3.5.
The low-pass filter from Figure 3.3 can be converted to the
z-domain using the forward Euler transformation.
