Frequency hopping sequences with optimal partial autocorrelation properties
We classify some p(k)-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p(2k) - 1 over a residue class ring R = GF (p) [xi]/(xi(k)) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p(k)-ary FH patterns of period p(2k - 1) are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by [L/pk+1] but the classified sequences achieve this bound with equality for any positive integer L.
frequency hopping partial autocorrelation finite rings generalized gordon-mills-welch (ggmw) sequences hamming correlation