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Quadriphase barker sequences

Started by Unknown September 29, 2005
Hello,

I am looking for a quadriphase Barker sequence (a sequence whose
elements are from the set {1,j,-1,-j} and which has a periodic
autocorrelation function whose maximum sidelobe magnitude <= 1). In
particular I am looking for a quadriphase Barker sequence of length 2^K
(integer K). Any help appreciated. (I've Googled a bit, but I can only
find polyphase Barker codes, where "poly" is greater than 4. In
context, I am looking for an easyily implementable synchronisation
sequence).

TIA

Slainte
Porterboy

<porterboy76@yahoo.com> wrote in message 
news:1127996535.217014.83710@g47g2000cwa.googlegroups.com...
> Hello, > > I am looking for a quadriphase Barker sequence (a sequence whose > elements are from the set {1,j,-1,-j} and which has a periodic > autocorrelation function whose maximum sidelobe magnitude <= 1). In > particular I am looking for a quadriphase Barker sequence of length 2^K > (integer K). Any help appreciated. (I've Googled a bit, but I can only > find polyphase Barker codes, where "poly" is greater than 4. In > context, I am looking for an easyily implementable synchronisation > sequence).
Hello Porterboy, While this may not be exactly what you want, you may wish to look up "complementary code keying." I think this will be close to what you want. This has a lot of the elements of Barker codes with some different optimality added. These are used in some of the 802.11 versions. Clay
Thanks Clay, I will indeed have a look at complementary code keying.

Just to let you know, I may have been chasing a dead end with my
original question. I just read something called the Mao Conjecture [1]
which says that for N = 0mod4 (which includes N = 2^K), the best
Quadriphase sequences have maximum sidelobe  of 2. This means that a
quadriphase barker sequence does not exist for N = 2^K.

[1] H. D. Luke et al, "Binary and quadriphase sequences with optimal
autocorrelation properties: a survey", IEEE Trans. Info Theory, Dec
2003, p. 3271.