Some days ago a friend of mine drop me an email asking about a signal recorded at 428 MHz. It's clearly an FSK modulation (probably GFSK) at the rate of 318124 bps as shown in Fig. 1, but the most interesting aspect was pointed out to me by my friend KarapuZ: he suggested me to investigate the signal in order to detect the presence of a scrambler. Indeed, after demodulation of the signal I found that a scrambler described by the polynomial x^9+x^4+1 was used.
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| Fig. 1 |
In normal usage, scrambling is used for two reasons:
1) it is used to remove the possibility of a long sequence of 1's and 0's in the bit sequence. The long sequence of 1's and 0's make timing synchronisation and clock synchronisation tougher at the receiver as regular transitions help in working of adaptive circuits like AGC and phase locked loop;
2) it eliminates the dependence of signal's power spectrum on the transmitted information sequence thereby keeping it below the maximum power spectral density requirement. If scrambling is not done, power might be concentrated in a narrow frequency band thereby causing intermodulation and crossmodulation distortion to adjacent channels.
2) it eliminates the dependence of signal's power spectrum on the transmitted information sequence thereby keeping it below the maximum power spectral density requirement. If scrambling is not done, power might be concentrated in a narrow frequency band thereby causing intermodulation and crossmodulation distortion to adjacent channels.
As a proof, KarapuZ kindly sent me two synthesized FSK signals: with and w/out the use of a scrambler. The used source bitstream and modulation are just the same of the real 428MHz signal. As you can easily see, the bitstream structure, if not scrambled, introduces an imbalance in the formation of the spectrum by a modulator (Fig. 2a) and the pseudo-random sequence originated by the scrambler "aligns" the spectrum (Fig. 2b): that's useful to us in order to understand the formation of signals.
For the sake of completeness, the spectrum of the 428MHz signal is shown in Fig 2c: note also that in the synthesized signals the Gauss filter was not used.
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| Fig. 2a - unscrambled signal, unbalanced spectrum in its low part |
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| Fig. 2b - same signal when scrambling is used |
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| Fig. 2c - 428MHz signal |
The same motivations seen above also apply to more complex signals which use PSK-n modulation.
Just to complete the analysis of the 428MHz signal, the source bitstream got after descrambling shows a 3420/6840 bits period that can be reduced to 18/39 bits patterns (Figs. 3,4).
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| Fig. 3 |
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| Fig. 4 |
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