Communication with Orthogonal Polyphase Signals over a Noisy Channel with Doppler Frequency Shift

A set of
N
orthogonal signals is constructed with a modulated carrier taking
N
possible phase values, and the whole class of such sets is described with a coding procedure that employs a permutation of
N
integers. These signals are used for communication purposes, and it is shown that there exists a simple matchedfilter detector with a coding and decoding scheme that is unaffected by a phase shift and a Doppler frequency shift on the channel.