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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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. Also, increasing transmitted power to improve accuracy is expensive and has a limited effect on multipath performance. Receiver design strategies such as very wide-bandwidth receiver front ends and very small early — late spacing in code-tracking discriminators provide diminishing returns at increasing cost.

In contrast, modulations designed specifically for radionavigation can outperform existing modulation designs while using the same or even less bandwidth and enabling simple transmitter and receiver designs. Further, more advanced modulations can better share existing frequency allocations with each other and with heritage signals, thus preserving spectrum. It remains important that modulations provide binary phase values, maintaining ease of signal generation including multiplexing multiple signals onto a single carrier and receiver processing.

These binary PSK modulations can readily be extended to higher-order alphabets. The binary offset carrier BOC modulation was developed for this purpose [2]. While BOC modulations were developed to provide spectral isolation from heritage signals modulating the same carrier frequency, it was quickly determined that they offer performance advantages as well. More recent work suggests that BOC modulations may allow yet another signal, in addition to heritage signals and the new military signal, to be added to currently allocated GPS bands [4].

While there has been previous consideration of subcarrier modulations for civilian signals e. The next section summarizes essential characteristics of BOC modulations. It defines the modulations, outlines the approach for generating them, and presents expressions for their second-order statistics. The third section introduces some example BOC modulations of particular interest, defines measures for evaluating characteristics of modulations for radionavigation, and evaluates these measures for the example BOC modulations.

Next, the paper outlines approaches for receiver processing of BOC modulations. It then presents results on effects of noise and of multipath on code-tracking accuracy, compared with equivalent results for PSK-R modulations. The final section summarizes the findings of this work.

Definition of Binary Offset Carrier Modulation The complex envelope of an offset carrier signal is given by [2] note that all the analysis here uses analytic signal representations and lowpass-equivalent representations of linear time-invariant systems :? The quantities? This representation shows that, when the spreading symbol is rectangular, offset carrier signals are conventional PSK-R signals modulating a periodic signal.

Initial work on offset carrier modulations focused on a sinusoidal subcarrier and a lowpass-filtered spreading symbol. The resulting complex envelope was not constant modulus. This class of offset carrier modulation has been termed linear offset carrier, since its modulus takes on a continuum of values. Implementation considerations motivated consideration of a square-wave subcarrier cTs t in equation 1 and a rectangular unfiltered spreading symbol?

The resulting binary-valued modulation, referred to as binary offset carrier, is the subject of this paper. There is a very close relationship between these variations of offset carrier modulations; in fact, a linear offset carrier modulation can be processed by a receiver using a BOC reference signal having the same subcarrier frequency and code rate with very little effect on performance. A BOC modulation is denoted BOC fs,fc , where fs is the subcarrier frequency, and fc is the code rate, defined by 1 fs?

The subcarrier frequency is actually? For example, BOC 10,5 means that the subcarrier frequency is Generation of data, spreading code, subcarrier, and RF uses a common clock so that zero crossings are aligned.

Figure 1 provides a block diagram of BOC signal generation. All of the baseband signals in Figure 1 are binary-valued, and thus can be implemented using binary logic. An equivalent representation to equation 1 describes a biphase BOC modulation as a PSK modulation with unconventional spreading symbol shape, so that its complex envelope can be written as?

Whenever n is even, qnTs t is a balanced average value of zero symbol. Considered in this sense, the BOC modulation generalizes a Manchester modulation to more than one zero crossing per spreading symbol i. Also, n? Spectra and Correlation Functions of Binary Offset Carrier Modulations Assume that the binary values of the BOC spreading sequence values are equally likely, independent, and identically distributed.

The appendix shows that for n even, the normalized unit area baseband power spectral density of a BOC modulation is? When n? Ts sin? In the power spectral density, the sum of the number of mainlobes and sidelobes between the mainlobes is equal to n, twice the ratio of the subcarrier frequency to the code rate. As in conventional PSK, the zero crossings of each mainlobe are spaced by twice the code rate, while the zero crossings of each sidelobe are spaced at the code rate.

For example, n? In contrast, n? Maxima of the mainlobes occur at frequencies somewhat below the subcarrier frequency because of the coherent interactions between the upper and lower sidebands. Examples of this point are provided in the next section. For an ideal BOC modulation with infinite bandwidth, the autocorrelation function consists of a set of connected line segments with in general multiple zero crossings and multiple lobes.

The number of negative and positive peaks in the magnitude autocorrelation function is 2n? Adopting the notation that? The zero crossings nearest the main peak occur at delay? For BOC 5,1 , n? The peaks are separated by The zero crossings nearest the main peak occur at approximately?

For BOC 5,2 , n? When the signal is ideally bandlimited to complex bandwidth? Gs f ei2? Gs f df?? The corresponding normalized correlation function for the bandlimited signal is?? When the RMS bandwidth is computed over finite bandwidth, two separate effects occur: loss of power and shaping of the spectrum.

To distinguish between the two, equation 13 defines the RMS bandwidth using the normalized bandlimited power spectral density, and the loss of power is accounted for separately through equation Lower Bound on Code-Tracking Accuracy A lower bound on code-tracking accuracy in white noise can be obtained using the RMS bandwidth [6], as a specific case of the more general lower bound in Gaussian noise and interference having arbitrary spectral shape [7, 8].

This lower bound is based on the performance of a maximum-likelihood estimator of time of arrival using T seconds of data, driving a tracking loop. The modulation has a normalized power spectral density Gs f over receiver front-end bandwidth?

N0 14 where the units of? LB are seconds. Define the spectral separation coefficient so that the composite interference has normalized power spectral density? The spectral separation coefficient having dimensions of seconds is then? Gs f df? Observe that when the spectral separation coefficient in equation 16 is computed for an interfering signal that is a unit-power sinu- soid at the frequency where Gs f attains a maximum value, Gs fmax? Since the emphasis in this paper is on modulation design, long spreading codes are assumed, leading to smooth spectra without spectral lines.

Signal characteristics provided below are computed for signals strictly bandlimited to 30 MHz bandwidth and normalized to unit power over that bandwidth. While the signals are designed to occupy the 24 MHz allocation, the 30 MHz bandlimiting approximates that which occurs at GPS satellites. The BOC 10,5 modulation was designed to allow the new military signal to be transmitted at much higher power while minimizing interference with existing signals and providing many other benefits, ranging from implementation ease to performance.

Before being selected, it was subjected to rigorous scrutiny, ranging from analysis to hardware demonstrations, as were other candidate modulations. Figure 3 portrays the spectra of The normalized scaled so that main peaks have unit height autocorrelation functions are portrayed in Figure 4, showing the narrower peak and multimode structure of the BOC 10,5 correlation function. Since it would serve as a new civil signal within L1 and L2, Vol.

Since n? The normalized autocorrelation functions are portrayed in Figure 6, showing the narrower peak and multimode structure of the BOC correlation function. The support of the BOC 5,2 autocorrelation function is half that of the autocorrelation function for 1. Although a Figure 7 portrays the spectra of BOC 8,4 and The normalized autocorrelation functions are portrayed in Figure 8, showing the narrower peak and multimode structure of the BOC correlation function.

Figure 9 shows the cumulative spectra of the five specific modulations being considered. All have most or all of their power contained within 24 MHz, but the different locations of large slopes show that their power is located in different portions of the band.

Table 1 provides the characteristics of these modulations. The locations of spectral peaks and their maximum power spectral densities are selfexplanatory. The 90 percent power bandwidth indicates the complex bandwidth needed to pass 90 percent of the signal power. Recall, as noted above, that these calculations use signals strictly bandlimited to 30 MHz, representing bandlimiting at the satellite, even though the signals are designed to use the Navigation Winter — Fig.

The smaller is the out-of-band power loss outside 24 MHz, the greater is the in-band power available to a receiver. The greater is the RMS bandwidth, defined in equation 13 , the better is the inherent ability to yield small code-tracking errors, under the assumption that the errors are small enough for linearized error analysis to apply.

The greater is the equivalent rectangular bandwidth, defined in equation 18 , the greater is the resistance to narrowband interference at the worst-case frequency. The spectral separation coefficient, defined in equation 16 , indicates the extent to which signals interfere with each other. In addition, a smaller spectral separation coefficient indicates the ability of a modulation to provide enough processing gain against multipleaccess interference from similar signals so that it can support higher data rates.

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## Binary offset carrier modulation

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.

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## BINARY OFFSET CARRIER MODULATIONS FOR RADIONAVIGATION PDF

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