A unified simulation approach for the fast outage capacity evaluation over generalized fading channels

The outage capacity (OC) is among the most important performance metrics of communication systems over fading channels. The evaluation of the OC, when Equal Gain Combining (EGC) or Maximum Ratio Combining (MRC) diversity techniques are employed, boils down to computing the Cumulative Distribution Function (CDF) of the sum of channel envelopes (equivalently amplitudes) for EGC or channel gain (equivalently squared enveloped/amplitudes) for MRC. Closed-form expressions of the CDF of the sum of many generalized fading variates are generally unknown and constitute open problems. In this paper, we develop a unified hazard rate twisting Importance Sampling (IS) based approach to efficiently estimate the CDF of the sum of independent arbitrary variates. The proposed IS estimator is shown to achieve an asymptotic optimality criterion, which clearly guarantees its efficiency. Some selected simulation results are also shown to illustrate the substantial computational gain achieved by the proposed IS scheme over crude Monte-Carlo simulations.