How does one compute the noise power to simulate real and complex GNSS signals?

Simulation of GNSS signals is very important to test and validate algorithms. With some algorithms, such as acquisition or tracking, we do not need to simulate a realistic constellation with actual ranges, Doppler or navigation data. We can simply simulate the signal after reception at a receiver’s front-end and only take into account and fix to desired values certain parameters, such as the intermediate and the sampling frequencies, the Doppler and Doppler rate, or the signal and the noise power. This last parameter requires some caution, because the noise power depends on the type of sampling (real or complex). In this article we show how to simulate noisy GNSS signals after a front-end. We will first present the model considered for the received signal and review the constraints on the intermediate and sampling frequencies for real and complex sampling. Then, we will introduce the noise, review the properties of a white noise, and discuss the sampling of a band-limited white noise to determine the expression of the noise power.