N-orthogonal phase-modulated codes
I.S. Reed, R.A. Scholtz · IEEE Transactions on Information Theory · 1966
In this paper biorthogonal codes are generalized in a natural way to a class of codes, calledN-orthogonal codes.N-orthogonal codes consist ofN^{M}signals divided intoN^{M-1}disjoint sets ofNsignals where signals in different sets are uncorrelated or orthogonal. One instance of theN-orthogonal codes is realized as a class of polyphase, constant-power modulated signals, the admissible phase set being denoted byN^{th}roots of unity. Matched filter receiver criteria for the Gaussian channel are developed and simplified integral expressions for the probability of error are derived.