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Importance sampling (IS) is a useful technique for reducing the number of Monte Carlo trials in BER estimation. Two important aspects of recent research work in this area are to find more applications of IS BER estimation and to seek a good bias scheme in the implementation of the estimator. This correspondence presents a general and rigorous mathematical description of these aspects of this problem which, we hope, will be useful for further research. We also present a general result on how to choose a good bias scheme which may provide some insight into the problem.