On Generalized Signal Waveforms for Satellite Navigation (797942), страница 55
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S. Orr and B. Veytsman, 2002], another field where majority voting hasattracted the interest of researchers in the past has been that of using the combination ofbinary codes for ranging applications. References dating to as early as 1962 can be found inworks from [M. F. Easterling, 1962], [D.J. Braverman, 1963], [R.C. Tausworthe, 1971] and[J.J.
Spilker, 1977]. These works describe how long codes with particularly well selectedproperties can be developed on the basis of shorter codes that are combined in an intelligentway. As it is well known, long codes are desirable to obtain good auto- and cross-correlationproperties. However, for acquisition, shorter codes are preferred to accelerate the process.Majority voting provides an efficient way to multiplex several short codes into a long codewith good properties.
The interest of this technique is that although the code presents amajority voted length that is in general by far longer than that of the individual codes itconsists of, there exists a substructure that can be used to quickly acquire one of the codes.This principle is in fact described by [M. F. Easterling, 1962]. In this work it is shown howseveral Pseudo Random Noise (PRN) sequences with prime periods can be majority voted toform a code with period the product of the individual components.
This longer code presentsimproved correlation characteristics but still preserves the substructure of the individual codesof shorter length, facilitating thus the acquisition.252Signal Multiplex Techniques for GNSSIt seems that, as shown in [A.R. Pratt and J.I.R. Owen, 2005], the majority votingmultiplexing technique has not been implemented yet in any real navigation system.Nonetheless we can find patents where this technique is employed combined with moresophisticated schemes such as the Interplex [G.L.
Cangiani et al., 2004]. We will refer tothese in chapter 7.8. Majority voting could play indeed an important role in the future, notonly for navigation, but also for terrestrial networks. The transmission of voice and data athigher rates than those that are possible today could be reality someday. As described by[R. S. Orr and B. Veytsman, 2002], the idea would be to transmit more than one code perservice in such a way that different code channels could be assigned to different functionssuch as pilot, paging, synchronization, control and traffic.
In addition, different powerallocations could be assigned to different services to avoid the dominance of one or a few.In addition, not only more services or channels could be transmitted multiplexed by themajority voted signal. In fact, different codes could be used too to transmit the same oneservice, enabling the operation of this service at higher data rates by splitting its data acrossthe different codes as shown by [R. S. Orr and B. Veytsman, 2002]. Indeed, if N codes areused to transmit the same service, each code could carry part of the data message and the totaldata rate would increase. Of course care has to be taken in making the code sufficiently long.The reason for this is that by having several codes running in parallel multiplexed within themajority voted signal, each code will suffer a slight degradation that will make thedemodulation more complicated.
However, this is by far compensated by the increase of thedata rate that can be achieved and by the fact that the correlation losses of any individualchannel are limited even when the number of signals to multiplex increases.Another interesting application that derives from the previous discussion could be the use ofmajority voting to transmit different codes with different lengths from the same satellite.
Thedifferent codes could have prime lengths and would be selected in such a way that they wouldbe optimum to serve specific applications. One can think, for example, of an indoor code, anurban-canyon code, codes with good acquisition properties or with good trackingcharacteristics. They would all be sent from the same satellite in an unique majority votedcode. From the receiver point of view, the particular user would only have to care about theparticular family of codes of interest being the rest of codes sent in the majority voted signalinvisible to him. For example, indoor receivers would have to correlate in the receiver withthe particular indoor codes of the constellation. These should be optimized in terms ofcorrelation properties. In the end, an indoor receiver working on indoor codes would not seethe effect of the other codes transmitted on the same satellite, except for a correlation loss ofnever more than 1.96 dB as we will show next.To conclude, it is of interest to mention that another highly desirable property of the subjectmultiplex method is its transparency to the receiver equipment in the sense that this does notneed to care about how the multiplex of the different signals looks like.253Signal Multiplex Techniques for GNSS7.4.2Definition of Majority VotingThe Majority Voting modulation, also known as Majority Combining, is a constant-envelopemultiplex technique based on majority-vote logic [J.J.
Spilker Jr. and R.S. Orr, 1998]. Themajority vote approach is basically a time-multiplexing of either the I or Q phases (scalar) orof both of them (vectorial) at the same time, where multiple signals are transmitted in a singleconstant envelope. The basic idea is that the time-multiplexed signal to transmit is selectedfollowing a particular logic based on the input signals. In its simplest form, namely theuniform weighting scalar distribution or equal weighting that will be described inchapter 7.4.4, the number of signals to multiplex must be odd to ensure majority in allpossible cases.
In this approach, the majority vote logic produces a multiplex where eachcomponent signal is equally weighted. In its most general form, namely the GeneralizedMajority Voting (GMV), any odd and even number of signals can be multiplexed in principlewith any possible weighting.Majority voting is a non-linear multiplex technique that provides a convenient and flexiblemethod to multiplex several signals into one constant envelope without multiplexing losses[J.J.
Spilker Jr. and R.S. Orr, 1998]. Moreover, it elegantly circumvents the peak versusaverage power trade that the lossless linear superposition presents when applied through acommon aperture, as we showed in previous chapter 7.3. The Majority Voting technique isalso of particular interest to secure acquisition of codes such as the M-Code where theinsertion of particularly well selected sequences would accelerate its detection. In the nextchapters, the true relevance of majority voting will be underlined by comparing thismultiplexing scheme with other better known techniques.7.4.3Theory on Majority VotingLet an odd number of binary spread spectrum codes be multiplexed as proposed by[J.J.
Spilker Jr. and R.S. Orr, 1998]. Majority logic operates on the principle that at a giventime point the value to transmit is that of the majority of the codes. For this reason, thenumber of component codes must be odd. According to this, if the codes share a commonchip rate, the majority voting operation will be done once per chip, while for the case that therates differ, the majority combination will occur at their least common multiple.If we think about the functioning of the majority logic, we can see that the majoritycombination rule is equivalent to computing the numerical sum of the code chips and takingits algebraic sign as shown by [J.J.
Spilker Jr. and R.S. Orr, 1998]. Indeed, for thecombination of three binary codes (c1, c2 and c3) the majority code, cMaj, can be as:cMaj =c1 + c2 + c3 − c1c2c32(7.7)254Signal Multiplex Techniques for GNSSOf course similar expressions can be derived for more codes, but the complexity increaseswith the number of signals to multiplex.
Furthermore, it is interesting to note that the previousequation can be used to derive the autocorrelation function of the majority voted signal andcorrespondingly the total spectrum as a function of the individual PSDs.The case that we have described in the previous lines is the simplest implementation of themajority voting logic. A generalization can be easily accomplished by means of interlacing,which is the insertion of chips of one or more of the component codes into the output chipstream as replacement for the corresponding majority chips as explained by[J.J. Spilker Jr.
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