Importance sampling for the efficient simulation of adaptive systems in frequency nonselective slow Rayleigh fading

Importance sampling (IS) is recognized as an efficient technique in reducing the simulation run time needed to estimate low bit error rates (BERs) in digital communication systems. In this paper. We present an IS stochastic gradient descent technique for the efficient simulation of adaptive systems which employ diversity in the presence of frequency nonselective slow Rayleigh fading and AWGN. After accounting for the overhead of the optimization algorithm, average speed-up factors of up to 6 orders of magnitude (over conventional Monte Carlo (MC)) were attained for error probabilities as low as 10/sup -11/.