Attention has been focused primarily on the design of the spreading code and selection of the keying rates. But better modulation designs are available for next-generation radionavigation systems, offering improved performance and the opportunity for spectrum sharing while retaining implementation simplicity. This paper describes a class of particularly attractive modulations called binary offset carrier BOC. Current modulation designs have been restricted to phase shift keying with rectangular spreading symbols referred to here as PSK-R , duplicating early modulation designs for digital communications. As other sources of error diminish, contributions from noise and multipath start to dominate. But bandwidth limitations preclude further improvements that might be obtained using PSK-R modulations with faster keying rates.

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In the next lines we will derive the general expression of the power spectral density. As we will see next, the matrix shows symmetry properties that will allow to simplify the problem considerably. It must be noted that the variable n refers to the number of subchips and not to the number of times that the sub-carrier contains the code rate as usually done in the literature. Betz, ] [2]. Taking as an example the sine-phased BOC signal of the lines above, we will derive now also a general expression by induction over n.

In this chapter we will derive general expressions to define the analytical shape of the autocorrelation function a generic BOC signal with infinite bandwidth.

This will help us understand the importance of having a good autocorrelation function in order to have good ranging potential for positioning. Additionally, analytical expressions will permit us establishing comparisons between sine- and cosine-phased BOC modulations and investigate the effect that extra terms in the definition of the ACF can bring. Before that, we derive first the inverse Fourier Transform of some functions of interest. The importance of these functions lies in the fact that since the Power Spectral Density of any MCS signal can be developed as a series with them, the derivation of analytical expressions for the ACF will be then possible no matter how complex the shape of the signal is.

Next we compare the BOC signal in sine and cosine phasing for different chip rates. For exemplification we will take a sub-carrier rate of As we can see, while the sine-phased concentrates more power at inner frequencies, so does the cosine version at outer frequencies. By looking at Figure 11 the following interesting properties can be observed: We can distinguish 6 peaks on every side with an amplitude of. This function shows the interesting property that we can easily convert the sine-phased autocorrelation function of any BOC signal into its cosine-phased counterpart by adding the corresponding difference function shown above.

As we can recognize, this spectrum is the difference between the power spectral densities of the sine-phased and cosine-phased BOC 15,2. BOC signals vs. These will be described in the following pages. As commented by [J. Avila-Rodriguez et al. Hein et al. In fact, this is the main idea behind the BOC modulation where a sub-carrier signal shifts spectral components to outer parts of the.

Betz and D. Goldstein, ] [8]. The relatively slow 1. Indeed many receiver implementations will make use of this principle to receive the future BOC signals.

Betz et al. This idea is also of interest to process the AltBOC. Rebeyrol et al. Rebeyrol, C. Macabiau, L. Lestarquit, L. Ries, J-L. Issler, M. Boucheret, M.

Betz, a] J. Weill, ] L. Weill, Multipath mitigation—how good can it get with new signals? Godet, ] J. Pratt and J. Owen, a] Anthony R.

Avila-Rodriguez, G. Hein, S. Wallner, A. Pratt, J. Owen, J. Betz, C. Hegarty, S. Lenahan, J. Rushanan, A. Kraay, T. Hein, J. Avila-Rodriguez, S. Goldstein, ] J. Betz, J. Fite, P.



Vojar However, since each of the two spectral sidebands redundantly contains all the information needed for ranging and data demodulation, the distinct sidebands can be processed separately if desired. For early radoinavigation late spacing of less than 45 ns, the code-tracking accuracy closely approaches the information-theoretic lower bound computed using equation 14indicating little benefit from using smaller early — late spacings. By providing almost 7 dB better spectral separation with itself than is provided by 1. Examples of this point are provided in the next section. The next section summarizes essential characteristics of BOC modulations.


Binary Offset Carrier (BOC)



Binary offset carrier modulation


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