For this class of distributions, the Gamma IS PDF with appropriately chosen parameters retrieves approximately, in the rare event regime corresponding to small values of $$\gamma $$ γ and/or large values of N, the same performance of the estimator based on the use of the exponential twisting technique. We aim to estimate the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb$$ b x p, for $$p>-1$$ p > - 1 and $$b>0$$ b > 0. For each case, we show numerically that the proposed state-dependent IS algorithm compares favorably to most of the well-known estimators dealing with similar problems. We apply our approach to the Log-Normal distribution to compute the OP at the output of diversity receivers with and without co-channel interference. Our proposed algorithm is generic and can be applicable without any restriction on the univariate distributions of the different fading envelops/gains or on the functional that is applied to the sum. In this line, we propose a state-dependent IS scheme based on a stochastic optimal control (SOC) formulation to calculate rare events quantities that could be written in a form of an expectation of some functional of sums of independent RVs. In this work, we use importance sampling (IS), being known for its efficiency in requiring less computations for achieving the same accuracy requirement.
Therefore, it is of paramount importance to use variance reduction techniques to develop fast and efficient estimation methods. However, this method requires a large number of samples for rare event problems (small OP values for instance). A naive Monte Carlo (MC) simulation is of course an alternative approach. In general, closed form expressions of expectations of functionals applied to sums of RVs are out of reach.
The outage probability (OP) at the output of Equal Gain Combining (EGC) and Maximum Ratio Combining (MRC) receivers is among the most important performance metrics that falls within this framework. When assessing the performance of wireless communication systems operating over fading channels, one often encounters the problem of computing expectations of some functional of sums of independent random variables (RVs).
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