A New Class of Spreading Codes Exhibiting Low Cross-Correlation Properties

Anthony R. Pratt

Abstract:	The present paper has been motivated by several objectives. The primary driver for this work has been the requirement to seek spreading codes for Galileo satellites which might be used to overlay GPS codes emitted on the L1 frequency band. This problem area also challenges GPS if more satellites are launched. A number of papers have been published (reference 1 is a recent example) in this general arena primarily analyzing signal types without identifying actual codes or the related code generator. These papers are characterized by using a cross interference model that relies on the envelope power spectral density of the spreading code type. For example, the envelope of a rectangular BPSK sequence (BPSK-R in ref 1) has a shape of {sin(x)/x}2 in frequency (x). In equivalent terms, any line structure in the codes is ignored, the code is assumed to be purely random with a continuous power spectral density function. Such an analysis is entirely justified by two assumptions: the spreading codes are very long, and many spectral lines of such a spreading code fall inside the code or carrier tracking loop of the target GPS receiver. In many cases, there is an opposing requirement that the spreading code be easy to acquire. This was the initial role for the CA code as a transitional mechanism to align and then track the P(Y) code. Such codes are characterized by their short repetition period. An example of these codes may be the proposed 10230 length code for possible use on GPS L5 (10.23MHz chipping rate, 1ms repetition period). In these cases, a line structure in the power spectral density of the spreading code is clearly evident. It can be argued that similar spreading codes in overlapping frequency space do not interfere if their spectral lines do not simultaneously appear within the tracking bandwidths of the receiver (code loop, carrier loop, etc). The present paper discloses a class of spreading codes with low cross-correlation properties with a defined set of existing spreading codes – the basis class. The properties of these classes of spreading code, built on a basis code class, show low cross-correlation properties with all members of the basis class. Specifically, the zero-Doppler cross-correlations are zero with the basis class. The cross-correlation properties between members of the new code class generally reflect the cross-correlation properties of the basis class. The zero cross-correlation condition is lost with Doppler offsets between the code classes as time-warping effects disturb some of the required intra-class restrictions. The new class of codes is based on certain inversions (implemented as a BOC modulation) of the basis codes and must have repetition periods that are exact multiples or sub-multiples of the repetition periods of the basis codes. It is shown that the only constraints that fall from the basis codes to the new code class are those of repetition period and the choice of the number of inversions as implied in BOC modulation. This implies that the new code class is rather rich in members and may be designed with substantially independent choice of mechanism and self cross- correlation properties. It is further shown that such codes perform significantly better in cross system interference than is predicted by the random code theory that has been widely used to date. This result has important implications in establishing the best mechanism for an initial sieve on code types and structure. Such properties may endear this class of codes to system designers as new satellite services start to evolve, and to those seeking to satisfy ITU mechanisms to ensure non-interference between satellite systems.
Published in:	Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) September 24 - 27, 2002 Oregon Convention Center Portland, OR
Pages:	1554 - 1564
Cite this article:	Pratt, Anthony R., "A New Class of Spreading Codes Exhibiting Low Cross-Correlation Properties," Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 1554-1564.
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