Military Communications and Information Technology: A Trusted ...
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Military Communications and Information Technology: A Trusted ...

Military Communications and Information Technology: A Trusted ... Military Communications and Information Technology: A Trusted ...

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502 Military Communications and Information Technology... Figure 5. The watermark decoder (extractor) The angle phase scanner searches for the drift values in the following set: 1 rad 1: : 1 100 s (3) Let us mark the number of watermark signal frames fed to the extractor input as M. Then, we can formulate the expression for the collective value of F iΔφ of i – pilot line after M of iterations (averagings): M F ReF ImF i ik ik k1 k1 M (4) The averaging occurs separately for the real and the imaginary part, with the established value of correction of Δφ angle phase, whereby the value of Δφ is constant for the entire set of M of iterations. The value of the virtual line module is derived from the following correlation: F v 6 F (5) i1 Having the information on the value of Δφ by which the current angle phase is corrected, we can read the value of the F vΔφ virtual line module from M iterations. i

Chapter 4: Information Assurance & Cyber Defence 503 The obtained maximum value of this line for set (3) enables us to determine the angle phase by which the phase has shifted against the host signal. After establishing the drift correction for frequency, the pilot samples used for reproducing the time synchronization undergo coherent averaging. Meeting the coherence requirement results in an increase of the spectral line amplitudes by reducing the noise deviation (of the host signal) for each iteration. Therefore, it can be demonstrated that, with the coherence requirement met, the value of the signal/noise ratio depends on the number of iterations (M) and is expressed by the following correlation: SNR dB 20log SNR 10log M (6) coh 10 coh 10 In order to correctly extract the binary signature on the receiver side it is necessary to divide the assayed signal frame into two subframes, whereby the moment of division should conform to the moment of division of the frame in the transmitter. Therefore, the receiver side requires time synchronization. The synchronization mechanisms used 8 pilot lines presented in fig. 3 (marked in blue). According to the proposed algorithm of time synchronization [9], in order to determine the time shift between the transmitter and the receiver of the watermark, two adjacent spectral lines are used (e.g. lines 16 and 17). In order to improve the accuracy of time shift determination, the synchronization procedure is repeated 4 times and the results undergo averaging. Assuming that the analyzed frame contains N = 1024 samples and the time shift between the transmitter and the receiver is m samples, the phase of the two adjacent linear samples will change by: 2 km 2 1 k , k m k1 (7) N N while the difference between those phases will be: 2m k 1 k (8) N Measuring the value of Δχ we can precisely determine the value of the time shift m between the transmitter and the receiver. Assuming that one signal period per signal frame with the established cardinality N is required to reproduce synchronization, then, in theory, the time shift value can be determined using only one harmonic – the first harmonic in the DFT spectrum. However, with N = 1024 and f s = 44 100 Hz, the first harmonic in the spectrum has the frequency of 43 Hz. With such low frequency value the signal degrades in the telecommunications channel; therefore, it is recommended to use two adjacent harmonics with higher frequencies, as explained in [9]. Furthermore, as pointed out in [9], the relative frequency difference between two adjacent spectral lines is exactly 2π; therefore, we can unequivocally assign the length of the N frame to this value. Fig. 6 presents the phase vectors for two adjacent harmonics (lines 16 and 17) in the transmitter and the receiver with the time shift m = 16 samples.

502 <strong>Military</strong> <strong>Communications</strong> <strong>and</strong> <strong>Information</strong> <strong>Technology</strong>...<br />

Figure 5. The watermark decoder (extractor)<br />

The angle phase scanner searches for the drift values in the following set:<br />

1<br />

rad<br />

<br />

1: : 1 100 <br />

s<br />

(3)<br />

<br />

Let us mark the number of watermark signal frames fed to the extractor input<br />

as M. Then, we can formulate the expression for the collective value of F iΔφ of i –<br />

pilot line after M of iterations (averagings):<br />

M<br />

F ReF <br />

ImF<br />

<br />

i<br />

ik ik<br />

k1 k1<br />

M<br />

(4)<br />

The averaging occurs separately for the real <strong>and</strong> the imaginary part, with<br />

the established value of correction of Δφ angle phase, whereby the value of Δφ<br />

is constant for the entire set of M of iterations. The value of the virtual line module<br />

is derived from the following correlation:<br />

F<br />

v<br />

6<br />

F<br />

(5)<br />

i1<br />

Having the information on the value of Δφ by which the current angle phase<br />

is corrected, we can read the value of the F vΔφ virtual line module from M iterations.<br />

i

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