We present an IS stochastic technique for the efficient simulation of adaptive systems which employ diversity in the presence of frequency nonselective slow Rayleigh fading and additive, white, Gaussian noise. The computational efficiency is achieved using techniques based on importance sampling (IS). We utilize a stochastic gradient descent (SGD) algorithm to determine the near-optimal IS parameters that characterize the dominant fading process. After accounting for the overhead of the optimization algorithm, average speed-up factors of up to six orders of magnitude [over conventional Monte Carlo (MC)] were attained for error probabilities as low as 10/sup -11/ for a fourth-order diversity model.

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 the IS parameters can be virtually impossible. We present a new IS optimization algorithm based on stochastic gradient techniques. The formulation of the stochastic gradient descent (SGD) algorithm 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 the 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).

Two importance sampling (IS) methodologies for Monte Carlo simulation of communication links characterized by time-varying channels and adaptive equalizers are presented. One methodology is denoted as the twin system (TS) method. A key feature of the TS method is that biased noise samples are input to the adaptive equalizer, but the equalizer is only allowed to adapt to these samples for a time interval equal to the memory of the system. In addition to the TS technique, the IA method, a statistically biased, but simpler, technique for using IS with adaptive equalizers that is based on the independence assumption between equalizer input and equalizer taps is presented. Experimental results show run-time speedup factors of two to seven orders of magnitude for a static linear channel with memory, and of two to almost five orders of magnitude for a slowly-varying random linear channel with memory for both the IA and TS methods.>