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