Digital Signal Processing Reference
In-Depth Information
energy in the first place. For this purpose, the output of the loop is equipped
with a saturation element. The complex-domain saturation block, clipping both
i-andq-signal values of the qpsk symbols, has a twofold objective. The first
task is to set a limit on the maximum signal energy that circulates in the loop of
the feedback system. The second and even more crucial task of this saturation
block is to force the output samples to adopt the shape of a qpsk constellation.
In this respect, one may consider the issr system as a nonlinear feedback loop
of which the output is a qpsk signal vector which is forced to have the same
spectral contents as the input signal vector, but only for those frequency bands
that contain legitimate information.
Since there is no explicit method to mathematically model such a complicated
hard-nonlinear system, the most appropriate approach to investigate the be-
haviour of the system under several conditions is by means of numerical sim-
ulations. However, even without digging deep into theory or simulations, it
is already possible to make some preliminary predictions about the stability of
the densely interconnected issr system: any positive feedback larger than unity
that would be present in the system shall eventually result in clipping of the out-
put vector. This clipping, which is due to the presence of the symbol-shaping
saturation elements, causes spectral components in the frequency bands that
are being blocked by the dft channel filter. As a result of this, energy begins
to leak out of the system which - indirectly - provides automatic gain control.
The whole idea of issr decoding is built around the assumption that every
possible sequence of transmitted symbols has its own specific spectral foot-
print. Extracting the original data from the received signal vector is then only
a matter of finding the most efficient way to map a particular spectral footprint
to its corresponding time-domain signal vector. Obviously, every imaginable
frequency-domain signal vector always has a valid corresponding time-domain
representation and so has any signal which is corrupted by isi or interference.
In order to allow the receiver to reconstruct the original time-domain signal
when its spectral footprint has been corrupted, a certain amount of redundant
information must be included at transmission side. In a classic fec coding
scheme, this goal is commonly achieved by transforming information bits into
data sequences of longer length. By allowing only a certain subset of sym-
bol sequences, the distance between two nearby sequences of a subset can be
increased. This offers the decoder the possibility to trace back to the correct
information. Identical to the principles of traditional error coding, it should be
possible to increase the minimum free distance between allowed signal foot-
prints in the frequency domain.
Fortunately, the redundancy required for this purpose is automatically embed-
ded at transmission side in the form of the modulation characteristic. The issr
decoder for qpsk modulation takes advantage of this knowledge by gently
