Stochastic gradient optimization of importance sampling for the efficient simulation of digital communication systems

Importance sampling (IS) techniques offer the potential for large speed-up factors for bit error rate (BER) estimation using Monte Carlo (MC) simulation. To obtain these speed-up factors, the IS parameters specifying the simulation probability density function (pdf) must be carefully chosen. With the increased complexity in communication systems, analytical optimization of IS parameters can be virtually impossible. In this paper, we present a new IS optimization algorithm based on stochastic gradient techniques. The formulation of the stochastic gradient descent (SGD) algorithm presented in this paper is more general and system-independent than other existing IS methodologies, and its applicability is not restricted to a specific pdf or biasing scheme. The effectiveness of the SGD algorithm is demonstrated by two examples of communication systems where IS techniques have not been applied before. The first example is a communication system with diversity combining, slow nonselective Rayleigh fading channel, and noncoherent envelope detection. The second example is a binary baseband communication system with a static linear channel and a recursive least square (RLS) linear equalizer in the presence of additive white Gaussian noise (AWGN).