Short Description

In Global Navigation Satellite Systems, such as GPS, every satellite is transmitting a particular pseudo-random noise (PRN) code, which is known at the receiver. Satellites are detected by correlating the received signal with local code replica: if the correlation exceeds a certain threshold, the satellite is assumed present. Due to transmission, the local replica differs from the received signal by a time lag and a Doppler shift. Both have to be determined in a two-dimensional search. This search is called “acquisition”, and is usually performed by partitioning the continuous search range into discrete cells.

In a previous work [1] we analyzed the influence of the number and width of Doppler bins on the detection performance of the GPS receiver, leaving all other effects (sampling frequency, quantization, data modulation of the satellite, etc.) aside. However, we promised that

“Future work will analyze the join of different aspects affecting detection performance (such as data modulation, statistical dependence of noise samples, oversampling, etc.) as well the effect of the Doppler bin width on computational complexity and mean acquisition time.”

In this project you should take a look at some (or all?) of these effects, derive a mathematical model, and validate it with the help of simulations.

Your Tasks

You should, depending whether you choose a project or a thesis analyze the effects of:

• Oversampling, i.e., the resolution in the time-lag-domain
• Data modulation, i.e., the fact that satellites transmit data all the time
• Statistical dependencies occurring in some FFT implementations (at least in terms of bounds)
• Quantization effects

Your Requirements

This work will be more on the theoretical side, MATLAB simulations will only be used for verification. Thus, a good background in probabilities and signal processing would be good. To have better start, we provide you with existing simulation codes and derivations.

References

[1]: Geiger, Bernhard C. and Vogel, Christian, “Influence of Doppler Bin Width on GPS Acquisition Probabilities”, submitted to a journal; preprint available: arXiv:1107.1972 [cs.IT], 2013.