On the construction ofN-ary orthogonal sequences under a continuous-phase constraint
Brian E. White · IEEE Transactions on Information Theory · 1973
Given the alphabetA = \{ \pm a_0, \cdots, \pm a_i, \cdots, \pm a_{N-1} \}the problem investigated is the construction of the largest set of mutually orthogonal sequences of lengthnunder the following constraint on the form of the sequences. Each sequence is a concatenation ofnelements fromAbut not all concatenations are allowed. Rather, the sign of thejth element is negative if and only if the(j - 1)st element is negative with an odd subscript, or the(j - 1)st element is positive with an even subscript. Such sequences have application in continuous-phase frequency-shift-keyed communication. The principal result is the construction of optimal sets of u (N,n)mutually orthogonal sequences under the phase constraint. Ifnis the order of a Hadamard matrix, then u = nN/2, forNeven, andn(N - 1)/2 + 1, forNodd.