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Periodic and aperiodic autocorrelation

Started by Treviasty June 14, 2010
Hello !

I'm starting experiments with compressed pulse radar and I have to choose
the best signal to transmit - low autocorrelation sidelobes, good ambiguity
function etc. . But there is one thing I can't understand - why there are
so many publications and researches about sequences with good periodic
autocorrelation ? After matched filtering of incoming single pulse I have
on the output the aperiodic autocorrelation, which has completely different
sidelobes than periodic one. If the pulse train had been used with matched
filter looking for single pulse, then periodic autocorrelation would be
visible on output, but it should result in train of periodic
autocorrelation pulses as well - I have never met this situation.

I would appreciate any hint.
Dominik


On Jun 14, 7:36=A0am, "Treviasty" <dominik.rzepka@n_o_s_p_a_m.gmail.com>
wrote:
> Hello ! > > I'm starting experiments with compressed pulse radar and I have to choose > the best signal to transmit - low autocorrelation sidelobes, good ambigui=
ty
> function etc. . But there is one thing I can't understand - why there are > so many publications and researches about sequences with good periodic > autocorrelation ? After matched filtering of incoming single pulse I have > on the output the aperiodic autocorrelation, which has completely differe=
nt
> sidelobes than periodic one. If the pulse train had been used with matche=
d
> filter looking for single pulse, then periodic autocorrelation would be > visible on output, but it should result in train of periodic > autocorrelation pulses as well - I have never met this situation. > > I would appreciate any hint. > Dominik
Sequences with low periodic autocorrelation are useful for direct- sequence spread spectrum (DSSS) systems. In such an application, the sequence in question is transmitted repeatedly with some additional information-based modulation applied. Thus, there is some periodicity to the transmitted waveform, and the periodic autocorrelation behavior of the sequence is important. You would like a sequence that has large spikes at maximum correlation, separated by periods of flat correlation that is as small as possible. An example of a family of sequences with this type of behavior is the Gold codes; they are used in the GPS system. This differs somewhat from the characteristics that you want for a radar pulse. In that case, you're looking for the presence of a pulse buried in the RF background only. In order to accurately detect the time of arrival of the pulse, you want a sequence whose aperiodic autocorrelation contains a single spike at maximum correlation and "nothing" at all nonzero lags. Apparently this is a much more stringent requirement than the periodic case, as optimal aperiodic correlation sequences, like Barker codes, are not particularly long. Jason
On 14 Jun, 13:36, "Treviasty" <dominik.rzepka@n_o_s_p_a_m.gmail.com>
wrote:
> Hello ! > > I'm starting experiments with compressed pulse radar and I have to choose > the best signal to transmit - low autocorrelation sidelobes, good ambiguity > function etc. . But there is one thing I can't understand - why there are > so many publications and researches about sequences with good periodic > autocorrelation ? After matched filtering of incoming single pulse I have > on the output the aperiodic autocorrelation, which has completely different > sidelobes than periodic one. If the pulse train had been used with matched > filter looking for single pulse, then periodic autocorrelation would be > visible on output, but it should result in train of periodic > autocorrelation pulses as well - I have never met this situation.
There are a number of possible reasons: - There are computational savings in the periodic computations compared to the aperiodic computations. - The academics who publish papers don't understand (or appreciate) the difference between idealized computations and real-world work - There are several radar pulses in the air at any one time - The radar signal is not pulsed but CW cyclic and so on. Rune

Treviasty wrote:
> Hello ! > > I'm starting experiments with compressed pulse radar and I have to choose > the best signal to transmit - low autocorrelation sidelobes, good ambiguity > function etc. .
STUDIOT, hehe. Haven't you learned yet that there is no such thing as "best" signal, and while improving one property you are compromising something else? If you use the word "best", you must clarify "best" with respect to what.
> But there is one thing I can't understand - why there are > so many publications and researches about sequences with good periodic > autocorrelation?
Those are used for data transmission. Those are simpler for analysis.
> After matched filtering of incoming single pulse I have > on the output the aperiodic autocorrelation, which has completely different > sidelobes than periodic one.
Of course.
> If the pulse train had been used with matched > filter looking for single pulse, then periodic autocorrelation would be > visible on output, but it should result in train of periodic > autocorrelation pulses as well - I have never met this situation.
So, what's the problem with that?
> I would appreciate any hint.
Google, wikipedia?
> Dominik
VLV