Improvement of noncoherent orthogonal coding by time overlapping

A simple way to increase the performance of noncoherent orthogonal coding is suggested. The idea is to overlap the transmitted symbols in time using an appropriate set of symbols. The best upper bound of the possible performance improvement in terms of E_b/N₀ when transmitting over the AWGN channel is proven to be M/(M-1). An example of a set of orthogonal symbols which can be overlapped to achieve this bound is the Walsh functions. The theory is a generalisation of the relation which exists between binary FSK and differential PSK for M-ary orthogonal noncoherent modulation