Digital Signal Processing Reference
In-Depth Information
integrator and by the sample period
T
s
of the discrete-time system. Once again,
note that this time interval is not related in any way to the symbol period of the
receiver. Parameter
T
s
has no associated physical meaning, but is related to the
step size of the algorithm. Reducing this step size will increase the accuracy of
the issr algorithm, but requires a higher number of iterations before conver-
gence will be reached. Finding a closed-form expression for the relationship
between accuracy, convergence time and gain
B
is not straightforward due to
the nonlinear nature of the loop. The same argument holds for gain element
A
,
so acceptable values for these parameters should be derived using numerical
simulations. A good initial value for both
B
and
A
was found to be very close
to unity.
Remark that when factor
A
is chosen equal to 1
.
00, the pole of the integrator
is located on the z-plane unity circle. The result is a marginally stable system
with a high risk to unbounded amplitude levels inside the loop. This can be
easily prevented by a restriction of the internal signal swing in the discrete-
time integrator. When considering the topology from Figure 3.4, this only re-
quires a relocation of the saturation blocks from the output of the issr loop to
the forward path of the discrete-time integrator. The final result, after a slight
repositioning of the delay elements, is shown in Figure 3.6. At this moment,
static input symbol vector (
n
samples)
Equalization filter
can be integrated.
in
1
in
2
in
n
ε
1
ε
2
ε
n
Controls accuracy of
ISSR algorithm.
DFT-based subband filter
B
B
B
Controls pole location
of the integrator.
Prevents unbounded
amplitude levels.
A
A
A
D
D
D
Allows to cut the
loop. Implement as
iterative algorithm.
out
1
out
2
out
n
ISSR output vector
Figure 3.6.
Discrete-time implementation of the issr loop. Some smart tuning
of the gain factors
A
and
B
can considerably speed up the conver-
gence process of the algorithm.
