A stochastic importance sampling methodology for the efficient simulation of digital communication systems with RLS adaptive equalisers

Obtaining a satisfactory precision on estimates of low bit error rates (BER´s) in digital communication systems using the conventional Monte Carlo (MC) method can be a prohibitive task due to long run time. While maintaining the same precision, importance sampling (IS) techniques can substantially reduce this run time using MC simulation. To obtain these speed-up factors, the IS parameters specifying the simulation probability density function (pdf) must be carefully chosen. The authors present an IS technique for the efficient simulation of baseband communication systems characterized by a static channel and a recursive least square (RLS) linear adaptive equalizer in the presence of additive white Gaussian noise (AWGN). This IS technique is based on a stochastic gradient descent (SGD) optimisation algorithm. Speed-up factors of 6 to 9 orders of magnitude over conventional the MC method were attained for error probabilities in the range of 10^-6 to 10^-9