The number of transmitted GNSS signals has increased significantly with Galileo, Compass and QZSS constellations' ongoing deployment, GLONASS constellation maintenance and the introduction of new GPS signals. The choice of new properties and features integrated in the corresponding new signal was driven by the need for compatibility and interoperability between signals and to provide better performance to the user. However, some aspects, which can be ignored with the old signals, should be discussed for these signals. For example, the code Doppler, caused by the satellite motion on the code frequency can be important for BOC modulation signals or signals with high code frequency. This plays a major impact on the performance of the acquisition and the tracking of GNSS signals and in particular weak signals. The acquisition is the first signal processing step in a GNSS receiver. It consists in giving a rough estimation of the incoming signals parameters (Doppler frequency and code delay). In the literature, many acquisition performance studies are derived assuming that there is no code Doppler on the received signal. However, the code Doppler leads to a change in the period of the spreading code that can lead to: * A drift between the received and local PRN codes even if they were synchronized at the beginning of the correlation process (correlation loss) * A possible drift of the correct acquisition bin over time. This can create missed acquisitions A positive Doppler shift causes the spreading code duration to shrink while a negative Doppler shift causes the spreading code duration to expand with respect to a reference that would not consider code Doppler. For example, for an incoming Doppler frequency of 10 kHz, for the GPS L1 C/A signal, it translates into a drift of 1 chip in 154 ms. For the same Doppler frequency, it translates into a drift of 1 chip every 12 ms for GPS L5. This result can cause a serious problem for acquisition of weak signals because long correlations (100, 200, 300 ms or more) can be required. The presence of a strong uncompensated code Doppler could thus create acquisition performance degradations because the autocorrelation function is degraded: the maximum amplitude is lower than the desired one and the correct code delay keeps drifted during the acquisition process. Besides, it is interesting to understand that for the same dwell time spent analyzing a specific acquisition bin, the impact on the acquisition depends on the acquisition technique and the choice of the coherent integration duration or the number of non-coherent summations. The detailed analysis of these effects is the topic of this paper. It encompasses: * An analytically analysis of the effect of code Doppler on the acquisition process and performance as a function of the signal characteristics and the acquisition parameters, highlighting the need to take this effect into account * Provide some techniques permitting to reduce the performance loss This paper specifically targets the new GNSS signals (Galileo E1 OS and GPS L5) which have different signal properties in terms of: code frequency (1.023 MHz and 10.23 MHz), modulation (BPSK, CBOC), carrier frequency (L1, L5)... The paper organization is the following: * The first section proposes a mathematical model of the correlation between the received signal (with Doppler shift) and the locally generated signal (assumed with no Doppler shift). The analysis of the mathematical model allows understanding the degradations in terms of acquisition performance. * The second section gives a specific study for several GNSS signals (GPS L1 C/A, Galileo E1 OS, GPS L5). This highlights practical values for the acquisition of these signals in terms of degradations and validity of the assumptions. For example, it is senseless to acquire non-coherently during 100 ms the GPS L5 signal because there are at least 8 chips shift. * To tackle this problem, several methods have been proposed in the literature and are reminded in the last section. For each method, a study of the solution against the code Doppler shift is done allowing understanding in which cases it is the most appropriate.