Perfect three-level and three-phase sequences and arrays
Leopold Bömer, Markus Antweiler · IEEE Transactions on Communications · 1994
Introduces construction methods for synthesizing new classes of perfect sequences and arrays. Time discrete sequences and arrays are perfect, if their periodic autocorrelation function sidelobes are zero. The construction of perfect three-level and three-phase sequences is performed in two steps. In the first step, a maximal length shift-register sequence with elements in GF(q) is built for a length of g/sup m//spl minus/1, where q is a prime power and m is a positive integer. In the second step, a sequence is constructed by mapping the elements of the shift-register sequence to 1, b/sub 1/ or b/sub 2/. Two real numbers b/sub 1/ and b/sub 2/ are determined such that the sequence becomes perfect and has high energy efficiency. The phase values for complex numbers b/sub 1/ and b/sub 2/ with magnitude 1 are given for perfect three-phase sequences. It is shown that the phase values of b/sub 1/ and b/sub 2/ tend for growing lengths to 2/spl pi//3 and 4/spl pi//3. A different similar synthesizing method starts with Legendre sequences. The construction of perfect three-level and three-phase arrays is performed by several methods, which make use of the new respective sequences.>