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On the construction of N -ary orthogonal sequences under a continuous-phase constraint

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Given the alphabet A = { \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 length n under the following constraint on the form of the sequences. Each sequence is a concatenation of n elements from A but not all concatenations are allowed. Rather, the sign of the j th 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 \nu (N,n) mutually orthogonal sequences under the phase constraint. If n is the order of a Hadamard matrix, then \nu = nN/2 , for N even, and n(N - 1)/2 + 1 , for N odd.

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IEEE Transactions on Information Theory  (Volume:19 ,  Issue: 4 )