A Geometric Interpretation Approach Tracing PN Sequence Code Phase Information and its Applications

Chieh-Fu Chang, Wan-Hsin Hsieh, Ming-Seng Kao

Abstract:	In this paper, we present a phasor-phase representation (PPR) approach to trace code phase shift, q, in PN sequence acquisition. The desired information q is explicitly identified in PPR approach, which is usually overlooked by conventional formula perspective in Convolution Theorem implementing serial search. First, the approach is based on the relationship between time shift information and phase of complex phasor developed from a single component of DFT (discrete Fourier transform). Then the approach is extended to give a geometric interpretation of Convolution Theorem (i. e., )(Y)(X]n[y]n[xF???????, where ? denotes convolution and F denotes Fourier transform) in complex domain. The desired information-code phase shift q is explicitly identified in our approach, which is imbedded in the phase of each phasor during each stage: Fourier transform, point-wise product operation, and inverse Fourier transform. The code phase information is explicitly traced, formulated, and represented geometrically in complex domain in each stage. Next, utilizing the geometric interpretation, the PPR approach enables us to develop more flexible and efficient algorithms than traditional approach. For example, PCA method [1] requiring only 6N complex additions, which uses much less computations than traditional FFT/IFFT approach requiring 2Nlog2N complex additions and 2Nlog2N complex multiplications. Also, the PPR grants us the geometric intuitive to further reduce computational load in each stage. Two promising techniques based on PPR approach are provided to enhance computational efficiency and combat sensitivity property to noise, respectively: 1. clipping phasor. 2. segmentation scheme. Furthermore, in order to illustrate the superiority of PPR approach, clipping phasor scheme is utilized to achieve anti-jamming for CW interference, partial-band interference and chirp interference. Besides, compared with the traditional frequency excision/notch filtering scheme, the clipping phasor scheme is simple and outperforms especially when the interference is not detectable. Finally, because of the associative superior computational efficiency, the PPR approach may be applied to unique pattern search in a long sequence. The potential applications in GNSS field include long PN code acquisition and revealing of a long encrypted code. The advantages and disadvantages of the PPR approach in applications are also discussed and the simulation will be provided to verify the analytical results.
Published in:	Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012) September 17 - 21, 2012 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	105 - 112
Cite this article:	Chang, Chieh-Fu, Hsieh, Wan-Hsin, Kao, Ming-Seng, "A Geometric Interpretation Approach Tracing PN Sequence Code Phase Information and its Applications," Proceedings of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, September 2012, pp. 105-112.
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