Inside GNSS Media & Research

JUL-AUG 2019

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36 Inside GNSS J U L Y / A U G U S T 2 0 1 9 mula, this means that a given section of the code is coherently integrated for , and then non-coherently accumulated N times, through the squared sum. e accumulation time is therefore , and the decision variable is: (30) e threshold is therefore obtained inverting a Non-Central Chi Square variable with 2N degrees of freedom, for a given false-alarm probability. One consideration is here necessary: in case of the "Time- Division" approach, the integration time coincides with the exact duration of the Authentication-Code integrated, because the code is continuous. In case of "Time-Hopping" approach the Authentication-Code is actually a watermarking of the Secure Navigation Code, and spread within it. For clar- ity, the notation indicates the length of the Authentication/ Code integrated coherently, for both TD and TH approaches. is means that for a given , the receiver needs to buff er a portion of signal long for the TD approach. For the TH approach, a portion of signal needs to be buff ered, with being the percentage of watermarking. is actually the observation window in which the coher- ent integration can be done. e observation window also indicates the interval adopted for code segmenting in the probabilistic key distribution approach. Expected Performance e model presented in the previous section allows to assess the expected performance of the technique, in standard AWGN channel, for the two approaches. In general terms, the two approaches are conceptually similar but their nature of packing vs spreading the chips make them diff er for the fol- lowing features: • Viable coherent accumulation time. Specifi cally, the TD allows longer coherent integrations because the observation window is signifi cantly shorter with respect to TH, when is the same. In other words, the channel fl uctuations have a minor impact in a small observation window, and this can be eff ectively exploited by the TD approach. • Processing time, or processing eff ort. is metric indicates the amount of time necessary to complete an authentication test. In general terms, the TH option has a processing time that increases linearly with time, under the assumption that the chips of the Authentication-Code are spread uniformly within the Secure Navigation Code. Equally, the number of operations done or the necessary buff ering. Conversely, for TD, the accumulation is achieved stepwise for each code block; unless one code block is suffi cient to complete one single test. In the latter case, TD can be signifi cantly faster, ideally times faster (with the same ). In more practi- cal terms, this metric is reasonably negligible in the overall Time To Authentication (TTA), that must cope with the fact that the data necessary to reconstruct the code is broadcast with some delay. WORKING PAPERS FIGURE 11 Probability of detection for a false-alarm probability of 10 -6 , with one accumulation. FIGURE 12 Probability of detection for a false-alarm probability of 10 -6 , with multiple accumulations.

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