Signal detection in the presence of weakly dependent noise--I: Optimum detection

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 on 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. The solution to this problem is then seen to be based on a linearly corrected version of the optimum independent-noise detection nonlinearity. The performance of this detector is compared to that of the corresponding optimum system for independent noise with the conclusion that performance gain is achieved by the proposed systems with no corresponding increase in complexity. Several specific examples are discussed to illustrate the types of noise environments for which this design technique is useful. Part II of this study will treat the problem of robust detection in the presence of weakly dependent noise.