Most of the previously reported studies of locally optimum (LO) detection in various noise environment have dealt with detection problems for independent samples. The use of an independent sample model may cause a considerable performance degradation in detection applications of modern high data rate communication systems exhibiting dependence among interference components. In this dissertation, we address the detection of weak known signals in observations corrupted by multiplicative and first-order Markov additive noise. The asymptotic and finite sample-size performance of several detectors are obtained and compared, confirming that the dependence among interference components need to be taken into account to maintain performance accordingly.