Mean acquisition time analysis for GNSS parallel and hybrid search strategies

Mean acquisition time (MAT) is one of the key performance indicators for the acquisition of global navigation satellite system (GNSS) signals. Usually, there are two stages in GNSS signal acquisition, called coarse acquisition and fine acquisition. A receiver starts the coarse acquisition with relatively large code-phase and frequency steps to obtain rough code-phase and Doppler estimates. Then, it follows a fine acquisition, in which the search steps are much smaller, to obtain the more accurate code-phase and Doppler estimates to meet the tracking loop requirements, and the search space is dramatically reduced. The existing MAT models only consider the coarse acquisition stage. We present the MAT expressions in consideration of both the coarse and fine acquisition stages. Also, our models are extended versions of the existing ones. The MAT expressions for three common GNSS signal acquisition schemes are provided, including parallel code-phase search (PCS), parallel frequency search, and hybrid search. The analytical expressions are verified by Monte Carlo simulations of GPS L1 C/A signals. We show how to optimize the acquisition parameters, including detection threshold, coherent integration time, and non-coherent integration time with the metric of MAT. The models facilitate not only MAT performance evaluation but also design parameter optimization of GNSS receivers.