Digital Signal Processing Reference
In-Depth Information
number of iterations will reduce the accuracy anyway. In the example from
above, increasing the step size by approximately 50% (
B
1
.
50) allowed to re-
duce the number of iterations from 12 down to 8 without noticeable impact on
the predetermined bit error rate performance (ber
≤
=
1
/
10
3
for E
b
/N
c
=
3dB).
Also shown in Figure 3.8 is a visualization of the qpsk symbol constellation
at the in- and output of the issr decoder. Before signal reconstruction, the
constellation points are spread over the entire signal plane as a result of the
effects of isi. During the reconstruction process, the data points slowly start to
cluster around one of the four qpsk constellation points. It is very intriguing
to observe how some of the sample points migrate to their final position, as
it is not necessarily the shortest path that is followed between their start and
end position. On the contrary, some sample points tend to move towards one
constellation point, then seemingly for no apparent reason 'decide' to switch
direction, in order to end up in one of the other three quadrants.
This behaviour is comparable to the behaviour of individuals observed in
par-
ticle swarm optimization
(pso) algorithms. At the start of the optimization
process, the particles have a large
cognitive
component which forces them to
propagate individually in the direction of the nearest constellation point (they
don't care about their fellow team members). After a few iterations of the issr
algorithm, most particles approach their optimum position. At this moment, the
residual energy in the error vector becomes dominated by those few particles
that were initially forced towards a wrong constellation point. Due to the ef-
fects of the integrator in feedback configuration, increasingly opposing forces
start to build up. This is where the
social
component of pso comes into play.
Most individuals in the swarm stay at their current position, since their com-
posite spectral signature resembles the required spectral footprint quite well.
Thanks to the joint forces of individuals in the swarm, only the few remaining
particles (qpsk symbols) with an adverse contribution to the spectral match
are driven to a new location in the constellation diagram. This despite the in-
dividual, cognitive component which initially forced them towards a wrong
constellation point.
Performance of ISSR in noisy channels
All previous simulations have been performed under the assumption that the
available fraction
F
of the transmission channel is completely free of additive
white Gaussian noise (awgn). In reality, the overall signal quality at the input
of the issr decoder is determined not only by the colored noise caused by the
elimination of isi or interference, but also by the thermal noise floor of the
channel. Define E
b
/N
0
as the bit energy per awgn power spectral density and
