Combinatorial Loss in Satellite Acquisition

Seppo Turunen

Abstract: Modern GNSS signal design strives for good cross-correlation and jamming resistance by specifying codes that are one to three orders of magnitude longer than the GPS C/A code. The downside of long codes is that they can be very hard to acquire in indoor areas and other places where satellite signals are heavily attenuated. The longest codes, such as the GPS L2C pilot code, may be infeasible for acquisition with present receiver technology, even in nominal conditions. It would seem natural to expect that the evolution of receiver technology towards faster parallel processing would eventually solve all acquisition problems. It should be realised, however, that limitations in receiver processing constitute only one part of the problem of acquiring long codes while another part is related to the inherent disadvantage of the long codes themselves. This disadvantage stems from the high false acquisition probability that is caused by a large number of search bins being involved in the acquisition process. The loss of sensitivity related to the false acquisition probability is referred to here as the combinatorial loss. Combinatorial loss is analysed here in the context of fully parallel acquisition. The analytic expression for false acquisition probability is derived with signal strength, search space size and the number of non-coherent processing steps as its parameters. The expression is then used to derive an approximate closed form functional relationship for the combinatorial loss and the size of the search space. Several numerical examples are given to illustrate the influence that search space size has on receiver sensitivity. The differences in code length are found to account for sensitivity differences of up to 10 dB in theoretical examples and up to 5 dB in practically motivated examples.
Published in: Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005)
September 13 - 16, 2005
Long Beach Convention Center
Long Beach, CA
Pages: 890 - 895
Cite this article: Turunen, Seppo, "Combinatorial Loss in Satellite Acquisition," Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2005), Long Beach, CA, September 2005, pp. 890-895.
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