10 September 2018

LINK-11 SLEW, properties of the acquisition preamble sequence

(thanks to Christoph for his Octave hints and collaboration) 

Since some weeks I'm studying the symbols sequence which is used to form the Link-11 SLEW acquisition preamble, the reason is that - quoting STANAG-5511 - "the acquisition preamble [...] consists of a 192 tri-bit known sequence generated from a pseudo random code": well, from waht I can see I don't think so. In my opinion the preamble sequence has been accurately studied and designed and in this post I try to argue the reasons.
The preamble sequence (used to define the start of a transmission, AGC, signal detection, synchronization, doppler requirements and equalization) is reported in S5515 as:

7 0 3 4 1 1 1 0 2 6 1 5 1 7 0 3 5 4 2 2 6 1 2 2 0 4 5 4 1 2 2 6
7 0 7 0 1 1 5 4 2 6 5 1 1 7 4 7 5 4 6 6 6 1 6 6 0 4 1 0 1 2 6 2
7 4 7 4 1 5 5 0 2 2 5 5 1 3 4 3 5 0 6 2 6 5 6 2 0 0 1 4 1 6 6 6
7 0 3 4 5 5 5 4 2 6 1 5 5 3 4 7 5 4 2 2 2 5 6 6 0 4 5 4 5 6 6 2
7 4 3 0 1 5 1 4 2 2 1 1 1 3 0 7 5 0 2 6 6 5 2 6 0 0 5 0 1 6 2 2
7 4 3 0 5 1 5 0 2 2 1 1 5 7 4 3 5 0 2 6 2 1 6 2 0 0 5 0 5 2 6 6

and according to #10.1.1.1 "these symbols are not scrambled and are applied directly to the 8 PSK modulator".


A first oddity - see Figure 1a - is that after the mapping of the complex symbols onto a PSK-8 constellation we don't get all the possible PSK-8 transitions as it happens for example by mapping the preamble sequence symbols of STANAG-4539 or a random sequence of PSK-8 symbols. A second puculiarity is that the preamble has a clear period of 96 bits (ie 32 tribit symbols) , which may be detected by BEE editor (see Figure 1b) and emphasized by plotting the matrix of complex symbols versus the columns (the two diagrams at the bottom of Figure 1a). 

Fig. 1a
Fig. 1-b

As a characteristic of PSK-n signals [1], the process of squaring a PSK-8 transforms the signal into a QPSK modulation (at twice the frequency); my friend Christoph pointed out to me that after the squaring of the preamble we get 6 repeating QPSK patterns, each 32 symbols long (1):

6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4


That's another oddity, or - better - another property of Link-11 SLEW preamble.

Christoph also noticed some other features of Link-11 preamble, but just the squared sequence is interesting for its "analogy" with the preamble used in STANAG-4285 (both consist of periodic sequences). 
Indeed, the periodic sequence of the squared preamble symbols can be assumed as a reference and - as it happens in S4285 - may be used to perform Doppler effetcs estimation by continuous correlation of the squared received sequence with the reference (S4285 adopts this method using the 31-symbol PSK-2 preamble sequence as reference for Doppler and sync acquisition [2]). Figure 2 shows the two reference sequences: notice the QPSK constellation of the squared L11 preamble. In my guess this is another point in favor of a designed preamble sequence.

Fig. 2
I wanted to look for evidences and confirmations from the analysis of a sample of a Link-11 SLEW signal [3], identifying and demodulating a preamble sequences (Figure 3).

Fig. 3

received preamble symbols:
5 6 0 6 3 4 2 7 1 6 3 1 5 1 7 0 4 0 3 2 6 1 2 2 0 4 5 4 1 2 2 6
7 0 7 0 1 1 5 4 2 6 5 1 1 7 4 7 5 4 6 6 6 1 6 6 0 4 1 0 1 2 6 2
7 4 7 4 1 6 5 0 2 2 6 5 1 3 5 3 5 1 6 2 6 5 6 2 0 0 1 4 1 6 6 6
7 0 3 4 5 5 6 4 2 6 1 5 5 3 4 7 5 4 2 2 2 5 6 6 0 4 5 4 5 6 6 2
7 4 3 0 1 5 1 4 2 2 1 1 1 3 0 7 5 0 2 6 6 5 2 5 0 0 5 0 1 6 2 2
7 4 3 0 5 1 5 0 2 2 1 1 5 7 4 3 5 0 2 6 2 1 6 2 0 0 5 0 5 2 6 6

after its squaring:

2 4 0 4 6 0 4 6 2 4 6 2 2 2 6 0 0 0 6 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 4 2 0 4 4 4 2 2 6 2 6 2 2 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 4 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 2 0 0 2 0 2 4 4 4
6 0 6 0 2 2 2 0 4 4 2 2 2 6 0 6 2 0 4 4 4 2 4 4 0 0 2 0 2 4 4 4


The difference between the reference and the received sequences are shown in Figure 4, notice that only the sequences #2 and #6 are received w/out errors.

Fig. 4
Figure 5 shows the results of the cross-correlations of the reference with the received sequences: the upper side concerns the tribit symbols while the lower side concerns PSK-8 symbols. I have to say that in this example the received PSK-8 symbols are not the actual ones since they are re-mapped at demodulation time; the tribit symbols instead are the actual ones.
Fig. 5
I am quite positive that the results would have been more complete and meaningful if I had extracted all the preamble sequences from the Link-11 transmission or if I had used only I/Q values. By the way, Christoph emailed me saying that he worked a link11 SLEW sample and the cross-correlations shows the expected results so that the doppler and frequency offset can be estimated: he's a skilled guy so hope to read soon such a post in his blog.

In conclusion, from what seen above, I do not think that Link-11 SLEW preamble is a sequence which is "generated from a pseudo random code" - by the way, so far I have not yet found a polynomial generator - but rather it seems a designed sequence or source algorithm (e.g. S4285 and S4539 do not talk of preamble sequences in such terms).


(1)
if "z" is a complex symbol and "s" is a tribit symbol, then:
z^2 corresponds to mod(2*s, 8)


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