Signal Detection in the Presence of Weakly Dependent Noise. Part I: Optimum Detection

摘要

The problem of discrete-time signal detection in the presence of additive noise exhibiting a weak form of dependence is considered. A moving average representation is used to model dependence in the noise sequence, and the degree of dependence is parameterized by the averaging weights. The weak dependence model is then based on the situation in which terms depending to second or higher order in the averaging weights can be considered to be negligible. Part I of this two-part study considers the problem of asymptotically efficient detection in this context for situations in which the noise statistics are known. An appropriate detector is sought by modifying the corresponding independent-noise detector structure in a way which does not increase detector complexity, and a corresponding weak-dependence design criterion is developed.