The reason for this drawback comes about due to the inefficient use of the noise generated in the
system. If n(t) is modeled as AWGN, denoted as N(0, 2), we see the majority of noise samples generated
will be centered at a voltage level of 0. These noise levels do not cause errors. It is the large
voltage levels that do cause errors; unfortunately, they rarely occur. It is for this reason that MC simulations
are computationally inefficient since they must be run for a long period of time in order to
give these rare events enough opportunity to occur [4??“7].
8.3 MODIFIED MONTE CARLO OR IMPORTANCE
SAMPLING METHOD
This next method involves a modification to the MC technique discussed above and is called the
Modified MC (MMC) or Importance Sampling (IS) in the literature [8??“11]. As discussed in the MC
section, the error-producing noise voltages rarely occur at high SNR values due to the PDF chosen.
Hence IS involves deliberate biasing of the noise statistics to artificially generate these errors or
important events. At the end of reception, the BER estimate must be unbiased to remove these effects.
Recall the following error event:
(8.22)
This equation can be rewritten as follows to introduce the biased form:
(8.
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