Simulations Based on System Abstractions
(Markov Modeling)

The use of abstract models typically results in simulations that run much faster than traditional Monte Carlo simulations. The hidden Markov model is the most often used abstraction. The mathematical foundations of the hidden Markov model are well understood and are analytically tractable. As shown in Figure 1, most systems have components that are defined at the bit or symbol level and other components that are defined at the waveform level. The channel is typically defined at the waveform level and simulation of the channel is often a process requiring considerable computational power. If the waveform portion of the system (shown in red in the simplified system model illustrated in Figure 1) can be replaced by a discrete channel model, the resulting system can be simulated at the bit or symbol level. This eliminates the need for sampling as well as the need for processing the resulting samples. Thus, the required simulation time is reduced by at least an order of magnitude.

Figure 1 - System illustrating discrete channel model.

The discrete channel model is often represented by a channel state transition diagram as illustrated in Figure 2. The model is defined through a set of transition probabilities, denoted aij. These probabilities are determined through channel measurement or through the execution of a waveform-level simulation. The model illustrated in Figure 2 is a four-state Fritchman model with three good states and one bad state. Models such as these have been successfully applied to a variety of wireless fading channels.

The advantage of hidden Markov models is that their use results in a significant reduction in computational burden. The disadvantage is that the hidden model is developed under a given set of conditions. If any system parameters within the waveform portion of the system are changed (bandwidth, modulation format, data rate, etc.), a new model must be developed.

Figure 2 – Four state channel model.