Semi-Analytic Simulation

The long run times often associated with Monte Carlo simulations are often very effectively mitigated through the use of semi-analytical techniques. The semi-analytic technique is applicable to any system in which the probability density function of the decision metric, such as the output of a matched filter, is known. The semi-analytic technique is most commonly applied to systems operating in a Gaussian noise environment in which the portion of the system between the point at which noise is injected to the point of the decision statistic is linear. The semi-analytic combines analysis and simulation. The decision metrics are first measured through the use of a noiseless simulation which, since noise is absent and therefore no statistical averaging must be done, is very short. The impact of noise is then accounted for analytically.

When a performance analysis of a communications system is to be developed, one often desires a display of the performance over a range of signal-to-noise ratios at the receiver input. This consideration points out another benefit of the semi-analytic technique. While the Monte Carlo method only provides a performance measure (bit error rate, frame error rate, etc.) at a given signal-to-noise ratio, the semi-analytic method provides performance measures over a range of signal-to-noise ratios. This is possible since the signal-to-noise ratio can be adjusted by an analytical scaling of the noise power, which is accounted for outside of the simulation.

The advantage of the semi-analytic technique is that simulations execute very rapidly and performance measures are obtained over a range of operating conditions with a single simulation. The disadvantage is that some analysis is required, and system model and noise statistics must be such that the required analysis can be accurately performed.