mohatta2015.pdf

192 SIMULATION NOTES
and noise realization. The corresponding received signal is then processed by one
or more equalization methods. The fading coefficients are not time-varying, but
remain constant for the duration of the transmitted signal. The process then repeats
with a different, independent fading realization.
To obtain a representative set of fading realizations within a reasonable simulation
time, the number of transmitted symbols is usually not very large. To achieve
good averaging over symbol and noise realizations, the symbols and noise are also
regenerated with each new fading realization.
The number of fading realizations to generate depends somewhat on the channel
and what aspect of the receiver is being studied. To obtain a good variety of fading
situations, a minimum of 1000 or 2000 fading realizations are recommended. To
obtain good agreement with analytical results, as much as 10,000 realizations may
be needed.
A.2 MATCHED FILTER AND MATCHED FILTER BOUND
Simulating the matched filter is straightforward, as the received signal is convolved
with the time-reversed conjugate of the channel response and sampled at the appropriate
times.
As for the MFB, closed-form analytical expressions can be used (we will label
these REF). One can also simulate the MFB (we will label these (MFB)). One way
is to generate an isolated symbol, surrounded by empty symbol periods. This is
the approach used in Chapter 2. Another way is perfectly subtract ISI from adjacent
symbols before applying MF. This latter approach is useful when simulating
fading channels, so that multiple symbols can be easily simulated for each fading
realization.
Sometimes we want to quantify performance in terms of an output SINR even
though we measure an error rate, such as symbol error rate. This is particularly
true when practical receiver aspects are considered as well as when nonlinear receivers
are used. We can introduce the notion of an effective output SINR (effective
output E s /N{)). We can compute this by measuring error rate and using analytical
relationships between error rate and E s /No to determine the effective E S /NQ.
A.3 SIMULATION CALIBRATION
It is important to calibrate one's simulator with independently generated results.
This was done for linear equalization by generating equivalent results for the channels
considered in [ProOl]. For these results, the linear equalizer uses 31 symbolspaced
taps centered on the first signal path. For consistency, 31 taps are used for
all symbol-spaced LE results in the remainder of this book.