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
Quadriphase barker sequences
Started by ●September 29, 2005
Reply by ●September 29, 20052005-09-29
<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
Reply by ●September 29, 20052005-09-29
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.