Abstract :
In a recent paper, a bound on the probability of runaway for a decision-directed receiver with unknown a priori probabilities was obtained. The analysis approximated the dependent learning process with a random walk model with independent increments. It is the purpose of this paper to demonstrate that by incorporating the central limit theorem into the above-mentioned analysis, a simple expression for a bound on the probability of runaway can be obtained. Furthermore, by applying a multivariate version of the theorem, the modified technique can be extended to analyze decision-directed receivers with several unknown parameters and the corresponding runaway bounds can be obtained. (By contrast, it is well known that multi-dimensional restricted random walk models are extremely difficult to study.) The results of this study again show that the probability of runaway is quite small even at moderate signal-to-noise conditions.
