Expansion of modulation for modulatable orthogonal sequences

Frank and Zadaff had proposed a class of polyphase orthogonal sequences. No w the sequences are called "Frank sequences." Suehiro has proposed a modula tion method for Frank sequences. For example, the number of 4-phase orthogo nal sequences of period 16 is 32 by Suehiro's method, on the other hand, th e number of 4-phase Frank sequences of period 16 is 2. In this paper, the m odulation method is expanded again and we prove that the sequences obtained by the proposed method are polyphase orthogonal sequences. Furhtermore, we prove that the number of N-phase orthogonal sequences of period N-2 Obtain ed by the proposed method is NN-2(N - 1)!. As a result of the proposed expa nsion, the number of 4-phase orthogonal sequences of period 16 is 96.