Simulation of Probability of Detection for the Delay-and-Multiply Method in GPS Signal Acquisition

The first step of the working process of a GPS receiver is signal acquisition, which is to detect the presence of the GPS signal and obtain necessary parameters for the tracking module. Many acquisition methods have been developed for various applications. Most of them require large numbers of steps to implement two-dimensional search for code-phase and frequency offset. The performance of these methods is affected by the Doppler frequency of the signal. The Delay-and-Multiply acquisition method avoids the effect of the Doppler frequency, and adopts a one-dimensional search process which significantly reduces searching steps. The method is thus suitable to be used in highly dynamic situations with high Doppler frequencies. However, the method has a disadvantage of introducing additional noise in the Delay-and-Multiply operation so as to lower the signal-to-noise ratio (SNR) and deteriorate the detection performance. This paper studies the performance of the Delay-and-Multiply acquisition method for GPS signal. Monte Carlo simulations are used to analyze the probability density functions of detected noise and signal. We have found that the distribution of noise is nearly Gaussian. The paper further calculates the probability of detection (Pd) and the probability of false alarm (Pf) according to the distributions of noise and signal, and presents the relations of Pd and Pf for different values of C/N₀. Compared to the traditional acquisition methods, the Pd is much lower under the same values of Pf and C/N₀ because of stronger noise. In order to improve the Pd, the noise is reduced by lowering the sampling frequency and extending the integration time. Simulation results show that the performance of the Delay-and-Multiply acquisition method is improved following the noise reduction.