Acquisition sensitivity limits of new civil GNSS signals

The challenge of signal acquisition does not depend only on the received signal power but also on the availability of reference time, reference frequency, satellite ephemeris information, and an initial location estimate. When available, they allow the receiver to calculate estimates for Doppler shifts and, if sufficiently accurate, for code phases. The estimates allow the receiver to reduce search ambiguity and the time and effort needed for acquisition. The reference time and reference frequency could, in principle, be obtained from a good crystal oscillator. However, the crystal oscillator of a consumer grade receiver is often prone to temperature drift and other instabilities. GNSS receivers that are integrated into a mobile phone have a high-quality frequency reference available from the cellular network. If the so-called assisted GNSS (A-GNSS) functionality is enabled, the receiver can also obtain time, location and satellite ephemeris information from the network. The required transactions are specified in all mobile telephone standards but the functionality has not, unfortunately, been implemented in all networks. The accuracy and content of the information is also dependent on the network.

Trends in receiver architecture

To successfully search and detect a GNSS satellite signal in an area of heavy fading it is often necessary to use an integration time of one second or more. This is true in particular when oscillator instability, signal modulation or receiver movement limits coherent integration time. Under such circumstances, a serial search would proceed extremely slowly except when accurate prior information about the code phases and Doppler frequencies is available. Modern consumer GNSS receivers are therefore more and more often equipped with a means of efficient parallel acquisition. A typical acquisition processor consists of a bank of time-domain matched filters for code phase searching and a digital Fourier transformer for frequency searching.

A recent trend is to use softwarebased acquisition and to perform the matched filtering in the frequency domain, which is computationally efficient. This kind of software acquisition is typically carried out off-line and the required transforms between the time and frequency domain are performed with FFT.

The processing of a delay-frequency bin for satellite acquisition is conceptually shown in Fig. 1. A stream of complex-valued baseband samples from the receiver RF section is multiplied with a locally generated replica signal to eliminate – or wipe off – the Doppler frequency and ranging code, leaving a complexvalued DC signal. The DC signal is then integrated coherently, squared, and added to a memory location dedicated to the specific combination of Doppler frequency and code delay. This sequence of operations, which constitutes one non-coherent processing step, is performed for each delayfrequency bin in parallel and repeated one or several times. Finally, a decision strategy is applied to the contents of the memory and a conclusion made about the existence of a satellite signal in one of the bins. If there is a known data modulation on the signal, it can also be wiped off. The wipe-off operations are linear so that their order of execution can be freely changed without effecting the end result, which is useful when optimising the HW implementation. Practical considerations, such as the availability of special signal processing elements, have resulted in widely different implementation architectures.

Numerous studies have been published about sequential acquisition strategies where the same hardware is allocated on different search bins at different times. An element frequently present in sequential strategies is multiple dwelling, where some bins are processed repeatedly to verify the acquisition results. Sequential strategies implicitly assume that acquisition performance is limited by the processing capacity. However, the rapid evolution of digital hardware is making the assumption less relevant. In fact, commercial receivers already contain real-time acquisition processors that can handle tens of thousands of delay-frequency bins in parallel, and SW receivers operating off-line with sample streams stored in memory do not even have strict hardware limitations. It is therefore interesting to know how acquisition performance is bounded when processing restrictions are removed and only physical limitations apply. It turns out that acquisition sensitivity then becomes heavily dependent on the length of the ranging code and on the availability of assistance information, a fact that has not been fully appreciated in the GNSS literature.

New civil GNSS signals and their acquisition strategies

The short C/A code was dedicated for acquisition and the longer P(Y) code for tracking in the original GPS specification. There is no similar division in the newer L1C [IS-GPS- 800], L2C [Fontana] and L5 [ISGPS- 705] civil signal specifications or in the Galileo OS [GJU] signal specification. Instead, all component signals have fairly long ranging codes and some of them also have high bit rates. These characteristics are likely to make acquisition difficult due to the resulting expansion of the search space and reduction of bit energy. The new specifications also include pilot signals that take up a significant fraction of the transmitted power. While it is thinkable that the unmodulated pilots are useful for tracking, it is questionable whether they can be used in acquisition due to their extremely long cycle lengths.

Table 1. shows the code lengths and other parameters of some present and future civil GNSS signals. The shortest ranging code belongs to the GPS L1 C/A signal and the longest to the GPS L2C pilot signal, the difference being approximately three orders of magnitude. Both codes are shift-register generated sequences that do not have a discernible substructure. As another example, the proposed Galileo L1 OS pilot signal has a concatenated ranging code consisting of a primary code with 4092 elements and a secondary code with 25 elements. Its cycle length is the product of the lengths of the component codes, i.e. 102300 elements.

The size of the acquisition search space is the product of four factors: the code length of the ranging code, the number of frequency search bands, the time domain over-sampling ratio, and the frequency domain over-sampling ratio. The number of frequency search bands is proportional to the coherent integration time since the latter is inversely related to the receiver bandwidth. In order to avoid code self-noise, the coherent integration time should normally be an integer multiple of code cycles. In the case of the GPS L2C pilot signal, this means that the shortest possible coherent integration time is 1.5 seconds. The coherent integration time for the GPS C/A signal is limited by data modulation to about 20 ms. It follows that the number of frequency search bands needed for the GPS L2C pilot signal is about 100 times larger than that needed for the GPS C/A signal, and further, that the size of the search space for the GPS L2C pilot signal exceeds that for the GPS L1 C/A signal by five orders of magnitude.