mohatta2015.pdf

138 MAXIMUM LIKELIHOOD SEQUENCE DETECTION
effective SINR (dB)
Figure 6.15 Cumulative distribution function of effective SINR for QPSK, root-raisedcosine
pulse shaping (0.22 rolloff). fading, two-tap, symbol-spaced channel, with relative
path strengths 0 and —1 dB, at fi dB average received Ει,/Νοpoints
easier to see). The line y = x is drawn to make it easier to see when one
equalizer is performing better than another.
When signal power is heavily faded (left portion of plot), we see that often MMSE
DFE performs worse than MMSE LE, due to decision error propagation. Moving
to the right of the plot, signal power increases and MMSE DFE does better, as
expected. At very high SINR, we see a "grid" of performance values. This is due to
the granularity issue discussed earlier. Some of the grid points occur below the line
of equal performance, indicating MMSE LE is performing better. However, recall
that we have few error events in this situation. Thus, the occurrence of these points
is probably due to not simulating enough symbols so as to accurately measure the
average symbol error rate. Keep in mind that for a particular fading realization and
particular symbol, different receivers can be better or worse than others, depending
on the ISI and noise realizations.
For completeness, a scatter plot for the power control case is given in Fig. 6.18.
Observe that the power reduces the variability in SINR, avoiding low SINR values
due to fading signal power.
6.4 MORE MATH
When symbols are sent in parallel, we end up with a vector form of the Viterbi
algorithm in which s(m) becomes a vector of symbols s(m). With multiple receive