# 3radio project - Part 5

* Linear-feedback_shift_register ( LFSR ) is a shift register whose input bit is a linear function of its previous state. A well-chosen feedback function can produce a sequence of bits that appears random and has a very long cycle ( en.wikipedia.org )*

In 3radio a LFSR is used to generate a pseudo noise whitening sequence that shows a sharp auto correlation function .

The Pseudo Random Noise (PRN) generator is implemented into an AT90USB162 uP.

I used a 31 stages long LFSR with 2 taps: [31, 28] in Fibonacci configuration. The generator output bits are computed in 8 bit burst and sent to the SPI serializer at a clock rate that can be selected between 2, 1, 0.5, 0.25, 0.125 Mbps. Some clock phase skewing is caused by the USB routine interrupts but it seems not affecting the resulting randomness. In the following the clock was set at 1 MHz.

The output sequence period is 2^31 -1 clocks = 2.147.483.647 microseconds = 2.147 seconds = 35 minutes

31 bit LFSR fits into a 32 bit integer and output period is long enough to easily cover the latency delay in between the tre RTL-SDR USB receivers.

The uP output signal is as follows:

The signal frequency shape (sinx/x)^2 depends on the rectangular bit shape with clk 1uS that has a spectrum with minimums at 1MHz division.

The measure shown in 3radio project - part 4 are repeated with different receiver frequency. It computes the cross correlation between sequences of 100000 samples.

Center frequency 69 MHz sampling 2.048 Msps

The pseudo randomness of the sequence improves the cross correlation results versus the previous test. Side lobes are low and the time latency between different RTL-SDR is within the 100000 bit analysis span used.

Center frequency 101.800 MHz sampling 2.048 Msps

Center frequency 144.000 MHz sampling 2.048 Msps

This measure shows the presence of a constant pattern that generates the triangular shape on the image on the left while on the right one it causes the minimum value offset.

I think the reason can be the presence of the 28.800 MHz x 5 = 144 MHz harmonic spur that it's synchronous and quite strong.

The following measure shows the results at 142000 MHz where there are lower spurs.

Center frequency 142.000 MHz sampling 2.048 Msps

Center frequency 500.000 MHz sampling 2.048 Msps

The correlation measure at 500 MHz shows that this frequency without a pulse shaping is the limit of the usable range and the peak value is 40 dB lower (100 times) than in VHF tests.

Possibly the use of a shape pulse circuit flattens the spectrum and increases the energy at higher frequency.

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