Comparative Study of Coherent, Non- Coherent, and Semi-coherent Integration Schemes for Gnss Receivers (preprint)

Three integration schemes, namely, coherent, noncoherent, and semi-coherent integration, and their variants are described in this paper for signal detection and tracking in such applications as pulsed Doppler radar and GPS receiver. We adopt a unified approach to present such integration schemes as best approximations to the likelihood ratio test (LRT) when the signal models are partially known to different extents. Formulas for the conditional probability density functions (pdfs) of the sufficient statistic under alternative hypotheses as well as the probability of detection (Pd) and probability of false alarm (Pfa) are given. Integration improvement factors and integration losses are then formulated. Connections of the semi-coherent integration scheme to the cyclic autocorrelation function, the discrete-time Wigner-Ville transform, and the radar ambiguity function are also outlined. Although most of the results are available in the literature, they are scattered in different textbooks and research papers. By presenting them in a cohesive and