N-orthogonal phase-modulated codes

In this paper biorthogonal codes are generalized in a natural way to a class of codes, called -orthogonal codes. -orthogonal codes consist of signals divided into disjoint sets of signals where signals in different sets are uncorrelated or orthogonal. One instance of the -orthogonal codes is realized as a class of polyphase, constant-power modulated signals, the admissible phase set being denoted by roots of unity. Matched filter receiver criteria for the Gaussian channel are developed and simplified integral expressions for the probability of error are derived.