Randomized Spectral Separation Coefficient for Short Code Acquisition Performance Evaluation

Reliable signal acquisition with low computational complexity is an important design objective for the evolution of global navigation satellite systems (GNSSs). Most GNSS signals consist of long pseudorandom noise (PRN) codes, whose acquisition is expensive in terms of memory, computation time, and energy. As these resources are particularly scarce in the emerging mass-market user segment, cyclostationary pilot signals with short PRN codes are an attractive option to keep the number of acquisition search bins low. However, reducing the code length degrades the acquisition performance, as multiple access interference (MAI) becomes more pronounced and can lead to an increased false alarm rate. We demonstrate that, quite different from stationary MAI, cyclostationary MAI does not affect each bin of the search space uniformly and is, therefore, not easily modeled with the well-known spectral separation coefficient (SSC). We propose a new randomized SSC (SSC-R) based on code/Doppler interference functions, which can be used for simple and accurate acquisition performance evaluation. As an application example, we demonstrate how the SSC-R can be utilized in signal design to minimize the PRN code length under an acquisition performance constraint. We conclude that feasible PRN code lengths for the GNSS can be on the order of 300–700.