The Sparse Fourier Transform: Theory and Practice by Haitham Hassanieh

Author:Haitham Hassanieh
Language: eng
Format: epub
Publisher: Association for Computing Machinery and Morgan & Claypool Publishers
Published: 2018-03-14T16:00:00+00:00

where t is time in seconds.

Like past synchronization algorithms, QuickSync must search and correct for the frequency offset in the received GPS signal in order for the correlation to spike at the correct code shift. However, since QuickSync processes p × n samples as opposed to n samples in past algorithms (see Section 8.3), it needs to deal with larger phase shifts that accumulate over pn samples. In order to overcome this limitation, QuickSync performs a finer grained frequency offset search, which introduces an overhead to the 2D search. This overhead, however, is amortized across all satellites in the GPS signal since correcting for this frequency offset is done on the received signal before it is multiplied by each satellite’s C/A code. In Section 8.7.2, we show that despite this overhead, QuickSync still provides a significant reduction in the computational complexity of GPS synchronization. Furthermore, the frequency offset changes slowly (see Section 8.7.2); hence, the receiver can cache its value from recent GPS readings, and does not need to search for it for every GPS synchronization event.

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