PERFECT N-PHASE SEQUENCES AND ARRAYS

Perfect sequences and arrays have a periodic autocorrelation function, whose out-of-phase values are 0. Time-discrete N-phase sequences and arrays have complex elements of magnitude 1 and one of (2-pi/N) n, 0 less-than-or-equal-to n < N, different phase values. In this paper, existence conditions and construction methods for perfect N-phase sequences and arrays with a small alphabet of possible phase values are introduced. Combining the existence conditions with methods of advanced computer search, new perfect N-phase arrays have been found. The resulting lowest number N of perfect N-phase sequences and arrays up to 40 elements are given in a table, after having applied the construction methods.