Abstract
AbstractA new class of coincidence (hit) arrays called cyclical hit arrays is defined. Cyclical hit arrays give insight into previously unknown properties of several sets of number theoretic frequency‐hop patterns, based on Welch‐Costas and Quadratic Congruence codes. Three theorems related to cyclical hit arrays are proved. The theorems are used to determine exact probability distribution functions of random variables which represent the number of coincidences between two arbitrary patterns from the same set of codes. The number of coincidences expresses interference levels between two users of code‐division multiple‐access (CDMA) systems which utilize the considered patterns. The obtained results can be used for computing the exact expressions for the total interference and for error probabilities in several CDMA systems.
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