Detection performance of complex lattice processors

Lattices are becoming increasingly important as the basis for new algorithms and as architectures for signal processors with applications in digital filtering, spectral estimation, speech processing, system identification and modeling, and many others. To date few studies have been carried out on the statistical performance of lattice processors, and only limited results are available. This paper presents new results in the use of complex lattice processors for detecting signals in noise. The approach is based on a detailed probabilistic study of the underlying complex reflection coefficients. Closed-form expressions and graphical results (ROC curves) are presented for the probability of detection and false alarm which allow an optimal choice of threshold setting.