VBOC2(a,1-a) Generalized Multidimensional Geolocation Modulation Waveforms

Abstract

, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of the publication of trade names, trademarks, service marks, or similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. This paper presents the complete original definition of first generation Variable Binary Offset Carrier 2(, 1 −) generalized multidimensional geolocation modulation waveforms, to improve the standardization of the United States DoD GPS, European Galileo, Russian GLONASS, Chinese Compass, Indian IRNSS in the L-band (1-2 GHz), and the United Nations International Telecommunications Union (ITU) GNSS or geolocation waveforms in the S-band (2-4 GHz) and C-band (4-8 GHz). In the paper it is argued that the selection of BOC(10,5) (or the military code or M-Code) on both GPS L1 and L2 frequencies is entirely arbitrary because BOC modulation is a special case of 2(, 1 −) for = 0 or = 1; hence, all the current state-of-the-art GNSS waveforms exhibit sub-optimal signal design performance even at the end-user when generalized global objective functions are applied. 2(, 1 −) pure signal design or broad definition of generalized autocorrelation function (ACF) and power spectral density (PSD) offers a unique signal design methodology and provides the necessary framework for 2(, 1 −) ACF pure signal optimization to fill in substantial signal design gaps; hence, improving the GNSS signal design and standardization.

VBOC2(a,1-a) ACF Pure Signal Optimization

“…Equations (1) (38) and (39) [3] or for all values of , = {2,4} and for = From (3) and (4), and = {2,4} we have …”

“…7 of [5] and then for the second time in [2] it was not until I started to design 2( , 1 − ) that it became apparent that 2( , 1 − ) pure signal design [3] and optimization offered unique challenges.…”

“…What are the unique and original challenges of 2( , 1 − ) pure signal design [3] and optimization that I believe so far have never been described in any other publication [7]- [27]? If we take a look at 2 (4 , , ) ( ) in Appendix B of Chap.…”

“…If you take a look at the generalized ACF of 2( , 1 − ) or 2 ( = , , ) ( ) in (38) or (39) of [3] for = 2 we notice that it contains eight non-zero terms; therefore, the ACF of 2( , 1 − ) or 2 ( = , , ) ( ) in (38) or (39) of [3] for = 4 needed to contain sixteen terms as shown in (38) or (39) of [3]. Hence, 2( , 1 − ) pure signal design [3] and optimization offered unique and original signal design and optimization challenges not encountered anywhere else.…”

VBOC1(a) ACF Pure Signal Optimization

“…The main objective of this paper is discuss : pure signal optimization: (1) for the first time ever in a journal publication is the discussion of a complete set of continuity theorems; (2) for the first time ever in a journal publication is the discussion of a complete set of optimization theorems; as a function of the signal design and optimization parameter, , and generalized parameter, which denotes the order of the .…”