This dissertation focuses on the importance sampling (IS) variance reduction technique in the Monte Carlo simulation of the performance of digital communication systems over a memoryless, additive Gaussian noise channel. The result is a unbiased estimate of the decision error with significantly smaller estimation variance than conventional Monte Carlo simulation provides. Several common digital ( n , k ) block codes are used to illustrate the importance sampling approach. Bounds on the variance of the error estimate are developed where the channel description is simple, but where the multiple dimension decision regions are potentially complex.
Coherent detection is used as a venue for the comparison of these IS techniques with respect to increasing dimension. Bounds based on the union bound are presented for several IS techniques. An overlap stratification variance reduction technique is introduced and extended with the application of IS. A mixed IS biasing function is employed for concentrating more samples in a particular error region and is employed for several of the common lower rate ([Special characters omitted.] < 1) block codes.
For the random phase channel the IS biasing function is developed as a 2 n dimensional pdf consisting of n Rayleigh-Rician pdf pairs. The error performance of several common lower rate block codes is presented. An alternate formulation, having the potential advantage of being able to use both mean translation and variance scaling, is presented. This approach is based on a commonly used technique to numerically generate a single Rayleigh-Rician pdf pair.
