Comparative Study of Coherent, Non-Coherent, and Semi-Coherent Integration Schemes for GNSS Receivers

Chun Yang, Mikel Miller, Erik Blasch, and Thao Nguyen

Abstract:	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 concise manner, the paper can serve as (1) an introductory material with key references for those who would like to study the subject further, (2) a quick reference for those who would like to compare these integration schemes, and (3) an integrated approach under varying conditions. Simulation results are presented to compare these integration schemes in terms of detection performance (Pd and Pfa) as a function of signal to noise ratio (SNR) and integration interval under two operating conditions. One is for a signal with constant Doppler frequency and the other is for a linear frequency modulation signal (i.e., a chirp signal). We show the curves of the input SNR required under different chirp rates so as to maintain the same detection performance, the resulting LRTs for the different approaches, as well as simulated comparisons between trade-offs of Pd versus SNR.
Published in:	Proceedings of the 63rd Annual Meeting of The Institute of Navigation (2007) April 23 - 25, 2007 Royal Sonesta Hotel Cambridge, MA
Pages:	572 - 588
Cite this article:	Yang, Chun, Miller, Mikel, Blasch, Erik, Nguyen, Thao, "Comparative Study of Coherent, Non-Coherent, and Semi-Coherent Integration Schemes for GNSS Receivers," Proceedings of the 63rd Annual Meeting of The Institute of Navigation (2007), Cambridge, MA, April 2007, pp. 572-588.
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