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cross-correlation of Walsh-Hadamard sequences overlayed with a PN sequence

Started by rge11x March 1, 2008
The cross-correlation of a few Walsh-Hadamard sequences are very good,
nearly ideal, but some are bad having very large sidelobes. Does
somebody know a systematic way to construct, or even a good table of,
a PN sequence that when overlayed with Walsh-Hadamard sequences, say
the 64-ary ones, the resulting 64 sequences will have, if not ideal,
at least uniformly low cross-correlation?

Thank you
"rge11x" <rge11x@netscape.net> wrote in message
news:c5da052f-b17d-4faf-9fce-80c2d9d25cd3@e60g2000hsh.googlegroups.com...

> The cross-correlation of a few Walsh-Hadamard sequences are very good, > nearly ideal, but some are bad having very large sidelobes.
What do you mean? The Walsh system is orthogonal hence the cross correlation is exactly zero.
> Does > somebody know a systematic way to construct, or even a good table of, > a PN sequence that when overlayed with Walsh-Hadamard sequences, say > the 64-ary ones, the resulting 64 sequences will have, if not ideal, > at least uniformly low cross-correlation?
This sounds like very general question. Good book: P. Fan "Sequence design for communication applications" Vladimir Vassilevsky DSP and Mixed Signal Consultant www.abvolt.com
On Mar 1, 4:04 pm, "Vladimir Vassilevsky" <antispam_bo...@hotmail.com>
wrote:
> "rge11x" <rge...@netscape.net> wrote in message > > news:c5da052f-b17d-4faf-9fce-80c2d9d25cd3@e60g2000hsh.googlegroups.com... > > > The cross-correlation of a few Walsh-Hadamard sequences are very good, > > nearly ideal, but some are bad having very large sidelobes. > > What do you mean? The Walsh system is orthogonal hence the cross correlation > is exactly zero.
The cross-correlation is zero when the the two Walsh-Hadamard sequences are exactly overlapping. When they do not then there can be large sidelobes as one slides by the other.
> > > Does > > somebody know a systematic way to construct, or even a good table of, > > a PN sequence that when overlayed with Walsh-Hadamard sequences, say > > the 64-ary ones, the resulting 64 sequences will have, if not ideal, > > at least uniformly low cross-correlation? > > This sounds like very general question. Good book: > > P. Fan "Sequence design for communication applications"
Thank you for the suggestion, I will check this book.
> > Vladimir Vassilevsky > DSP and Mixed Signal Consultantwww.abvolt.com

rge11x wrote:

> On Mar 1, 4:04 pm, "Vladimir Vassilevsky" <antispam_bo...@hotmail.com> > wrote: > >>"rge11x" <rge...@netscape.net> wrote in message >> >>>The cross-correlation of a few Walsh-Hadamard sequences are very good, >>>nearly ideal, but some are bad having very large sidelobes. >> >>What do you mean? The Walsh system is orthogonal hence the cross correlation >>is exactly zero. > > The cross-correlation is zero when the the two Walsh-Hadamard > sequences are exactly overlapping. When they do not then there can be > large sidelobes as one slides by the other.
Not much can be done if the signals are asynchronous. This situation is avoided in the communication systems since it results in the tremendous drop in the channel capacity. IIRC the theoretical limit for this case is only 18% of Shannon. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com

rge11x wrote:


>>>The cross-correlation of a few Walsh-Hadamard sequences are very good, >>>nearly ideal, but some are bad having very large sidelobes. >> >>What do you mean? The Walsh system is orthogonal hence the cross correlation >>is exactly zero. > > The cross-correlation is zero when the the two Walsh-Hadamard > sequences are exactly overlapping. When they do not then there can be > large sidelobes as one slides by the other. > >>>Does >>>somebody know a systematic way to construct, or even a good table of, >>>a PN sequence that when overlayed with Walsh-Hadamard sequences, say >>>the 64-ary ones, the resulting 64 sequences will have, if not ideal, >>>at least uniformly low cross-correlation?
The signals can be separated either in time or in the frequency domains, or both in time and frequency. If the signals can slide in the time domain arbitrarily, then they have to occupy the different frequency bands. The worst case cross correlation equals to the amount of overlap of the time-frequency patterns. In the other words, you have to design the sequences so their spectra would have the controlled amount of overlap. Fourier series are the immediate solution. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com