Hello,

I'm looking for a spreading code that I can output from a microcontroller 
(PIC). The sequence must have low autocorrelation with a good merit factor. 
It should be a long sequence of between 4000 and 20000 and does not have to 
be done with a LFSR (shift register) since I have lots of code space left 
and I can just hard code it into memory. Therefore it does not have to be a 
2^N value.

My first question is fundamental...does a low autocorrelation sequence give 
you a flat-ish power spectral density? Or are some sequences better for 
spreading while others are better for correlation?

My second question is, does anyone know of an online resource of large 
sequences with good merit factors? (I found one awhile back, but can't seem 
to find it now)

Thanks,
Thomas 

Thomas Magma wrote:

> Hello,
> 
> I'm looking for a spreading code that I can output from a microcontroller 
> (PIC). The sequence must have low autocorrelation with a good merit factor. 
> It should be a long sequence of between 4000 and 20000 and does not have to 
> be done with a LFSR (shift register) since I have lots of code space left 
> and I can just hard code it into memory. Therefore it does not have to be a 
> 2^N value.

If the goal is having a good ACF, you can take pretty much any random or 
quasi-random sequence. Some sequences could have better ACF then the 
others however there is not going to be much of a difference if the 
sequences are that long.

There could be many other application dependent considerations for the 
sequence design, too.

> My first question is fundamental...does a low autocorrelation sequence give 
> you a flat-ish power spectral density?

Fundamental answer: yes.

> Or are some sequences better for 
> spreading while others are better for correlation?

It depends. Better for what application?

> My second question is, does anyone know of an online resource of large 
> sequences with good merit factors?

online == bullshit

> (I found one awhile back, but can't seem 
> to find it now)

P. Fan, M. Darnell. “Sequence design for communications applications”
John Wiley & Sons
ISBN 0-471-96557



Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

On Aug 20, 1:25 pm, "Thomas Magma" <somewh...@overtherainbow.com>
wrote:
> Hello,
>
> I'm looking for a spreading code that I can output from a microcontroller
> (PIC). The sequence must have low autocorrelation with a good merit factor.
> It should be a long sequence of between 4000 and 20000 and does not have to
> be done with a LFSR (shift register) since I have lots of code space left
> and I can just hard code it into memory. Therefore it does not have to be a
> 2^N value.
>
> My first question is fundamental...does a low autocorrelation sequence give
> you a flat-ish power spectral density? Or are some sequences better for
> spreading while others are better for correlation?

By the Fourier transform properties, things that are narrow in
one domain is spread out in the other.  That said, you can
explicitly search for sequences to optimize their autocorrelation
properties.

>
> My second question is, does anyone know of an online resource of large
> sequences with good merit factors? (I found one awhile back, but can't seem
> to find it now)

Try searching for "Barker sequences".

>
> Thanks,
> Thomas

>
> Try searching for "Barker sequences".
>

The longest known Barker Code has a length of 13, I need lengths three of 
four magnitudes greater than that.

Thomas 

On Aug 21, 6:15 pm, "Thomas Magma" <somewh...@overtherainbow.com>
wrote:
> > Try searching for "Barker sequences".
>
> The longest known Barker Code has a length of 13, I need lengths three of
> four magnitudes greater than that.
>
> Thomas

So do a search for other sequences.  Barker sequences
are defined by its optimality.  There is debate about whether
a Barker sequence exists for really large lengths, so you know
your limits!

This is a problem that only has to be done once, so it's worth
keeping your computer humming for a while, depending on
your constraints.

Julius

> This is a problem that only has to be done once, so it's worth
> keeping your computer humming for a while, depending on
> your constraints.
>

I think it might blow the budget of my project if I were to rent a super 
computer to run for 5 or 10 years to do what you suggested. However if I did 
discover a large Barker sequence, I would probably forget about my project 
and sprint down to the closest patent office.

How long would it take your computer to iterate through all the possible 
combinations of 2^65536 determining the merit factor of each?

Thomas 

On Aug 20, 1:25 pm, "Thomas Magma" <somewh...@overtherainbow.com>
wrote:
> Hello,
>
> I'm looking for a spreading code that I can output from a microcontroller
> (PIC). The sequence must have low autocorrelation with a good merit factor.
> It should be a long sequence of between 4000 and 20000 and does not have to
> be done with a LFSR (shift register) since I have lots of code space left
> and I can just hard code it into memory. Therefore it does not have to be a
> 2^N value.
> ...............
>...................
> My second question is, does anyone know of an online resource of large
> sequences with good merit factors? (I found one awhile back, but can't seem
> to find it now)


A Legendre sequence rotated by one-fourth of the period has a merit
factor of
about 6 (asymptotically).  This is about the best result known for
specifically
constructible sequences, though there has been some work on adding a
few bits at the end of the Legendre sequence (like a cyclic extension
in
other contexts) to improve the merit factor to somewhat more than 6.

T. Høholdt and H.E. Jensen. Determination of the merit factor of
Legendre sequences.
IEEE Trans. Inform. Theory, 34:161-164, 1988.

J. Jedwab. A survey of the merit factor problem for binary sequences.
In T. Helleseth
et al., editors, Sequences and Their Applications - Proceedings of
SETA 2004, vol-
ume 3486 of Lecture Notes in Computer Science, pages 30-55. Springer-
Verlag, Berlin
Heidelberg, 2005.

Hope this helps.